The expression [tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx[/tex] is an illustration of definite integrals
The approximated value of the definite integral is 0.0059
How to evaluate the definite integral?The definite integral is given as:
[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx[/tex]
For arctan(x), we have the following series equation:
[tex]\arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1}}{2n + 1}}[/tex]
Multiply both sides of the equation by x^3.
So, we have:
[tex]x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1}}{2n + 1}} * x^3[/tex]
Apply the law of indices
[tex]x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1 + 3}}{2n + 1}}[/tex]
[tex]x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}[/tex]
Evaluate the product
[tex]x^3 \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}[/tex]
Introduce the integral sign to the equation
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =\int\limits^{1/2}_{0} \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}[/tex]
Integrate the right hand side
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}} ]\limits^{1/2}_{0}[/tex]
Expand the equation by substituting 1/2 and 0 for x
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}} ] - [ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{0^{2n + 4}}{2n + 1}} ][/tex]
Evaluate the power
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}} ] - 0[/tex]
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}}[/tex]
The nth term of the series is then represented as:
[tex]T_n = \frac{(-1)^n}{2^{2n + 5} * (2n + 4)(2n + 1)}[/tex]
Solve the series by setting n = 0, 1, 2, 3 ..........
[tex]T_0 = \frac{(-1)^0}{2^{2(0) + 5} * (2(0) + 4)(2(0) + 1)} = \frac{1}{2^5 * 4 * 1} = 0.00625[/tex]
[tex]T_1 = \frac{(-1)^1}{2^{2(1) + 5} * (2(1) + 4)(2(1) + 1)} = \frac{-1}{2^7 * 6 * 3} = -0.0003720238[/tex]
[tex]T_2 = \frac{(-1)^2}{2^{2(2) + 5} * (2(2) + 4)(2(2) + 1)} = \frac{1}{2^9 * 8 * 5} = 0.00004340277[/tex]
[tex]T_3 = \frac{(-1)^3}{2^{2(3) + 5} * (2(3) + 4)(2(3) + 1)} = \frac{-1}{2^{11} * 10 * 7} = -0.00000634131[/tex]
..............
At n = 2, we can see that the value of the series has 4 zeros before the first non-zero digit
This means that we add the terms before n = 2
This means that the value of [tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx[/tex] to 4 decimal points is
[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.00625 - 0.0003720238[/tex]
Evaluate the difference
[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.0058779762[/tex]
Approximate to four decimal places
[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.0059[/tex]
Hence, the approximated value of the definite integral is 0.0059
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Find two examples of hyperbole in chapter 5 the watsons go to birmingham
An example of hyperbole that were written in chapter 5 of "The Watsons go to Birmingham" include the following:
The whole upstairs smelled like a giant match.What is hyperbole?Hyperbole can be defined as a figure of speech (figurative language) that connotes an unintentional or deliberate exaggeration (overstatement) of a situation, an event or thing by a writer of a literary work.
Two (2) examples of hyperbole that were written in chapter 5 of "The Watsons go to Birmingham" include the following:
The whole upstairs smelled like a giant match.They had to wear clothes that smelled like smoke for two years because their house caught fire.Read more on hyperbole here: https://brainly.com/question/23459635
What obstacle was faced by the union pacific railroad workers but not the central pacific workers? steep mountains conflict with american indians harsh weather conditions worker shortages
An obstacle which was faced by the union pacific railroad workers but not the central pacific workers is: B. conflict with American Indians.
Who are union pacific railroad workers?The union pacific railroad workers can be defined as a group of young Civil War veterans and Irish immigrants that were saddled with the responsibility of providing railroad related services to commuters.
Unlike the central pacific workers, an obstacle which was directly faced and experienced by the union pacific railroad workers is conflict with American Indians (Native Americans) because the American Indians wanted to reclaim the jobs and way of life that was being taken away from them.
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I know I am a week late but for the future people the answer is A,C,D,F.
I got it right on edge.
The other aswer to the second question is B.
Got it right on edge, Have a good day <3.
Which mathematical word describes both 27 x and 6 x in the expression 27 x + 6 x ?
The climate in northern alaska suddenly changes from a very cold climate to a warm climate. Two species of wolves live in this area. Species x has long fur and doesn't shed to regulate internal temperature. Species y has short fur and sheds to regulate internal temperature. Which species is most likely to survive this climate change?
Answer:
Both species will survive because they have fur to help maintain constant internal temperatures.
Explanation:
brainly pls
If this scenario continues, what do you think will happen to the populations in the next 100 years? why do you think this might happen?
when activated phospholipase c cleaves an inositol phospholipid, what happens to the small signaling molecules the enzyme produces?
When activated phospholipase c cleaves an inositol phospholipid, Both inositol 1,4,5-trisphosphate (IP3) and diacylglycerol are retained in the membrane.
What occurs if phospholipase C is activated?When G protein is said to be stimulated, it is known to often activates phospholipase C.
Note that phospholipase C. is siad to hook up to a phospholipid known as phosphatidylinositol 4,5- biphosphate that is often seen in the plasma membrane lipid bilayer. The outcome of thses two hookup is the production of two products known as inositol 1,4,5 triphosphate (IP3) and diacylglycerol (DAG).
See options below
hen activated phospholipase C cleaves an inositol phospholipid, what happens to the small signaling molecules the enzyme produces? Choose one:
A. Both inositol 1,4,5-trisphosphate (IP3) and diacylglycerol are released into the cytosol.
B. Inositol 1,4,5-trisphosphate (IP3) remains in the membrane, while diacylglycerol is released into the cytosol.
C. Both inositol 1,4,5-trisphosphate (IP3) and diacylglycerol are retained in the membrane.
D. Inositol 1,4,5-trisphosphate (IP3) is released into the cytosol, while diacylglycerol is retained in the membrane.
E. Both inositol 1,4,5-trisphosphate (IP3) and Ca2+ are released into the cytosol.
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Introduction to linear algebra 4th edition solutions
Answer:
Whats your question?
What do you need help on?
I took algebra a while ago so I may be able to help you.
You must be at least 48 inches tall to ride the bumper cars
Answer:
h>=48
Explanation:
let h be height
h >= 48
It is generally believed that nearsightedness affects about % of children in a certain region. a school district tests the vision of incoming kindergarten children. how many would be expected to be nearsighted? what is the standard deviation for the number of nearsighted children in this group?
True or false if a and b are square matrices, then ab =ba,
yes
Explanation:
it is true because it's the formula of mathematics
The doppler effect indicates that the universe is expanding because_________. which phrase best completes the sentence.
Answer: light from other galaxies is red.
Explanation: Astronomers have observed that light from the distant object in the universe is shifted towards the frequency of red color which indicates that those object are receding or moving away from the planet earth.This phenomena was termed as Red shift .Same thing goes for galaxies which are very far away from the planet earth.
Where as if galaxies were moving towards the the planet earth their light would have shifted toward the frequency of blue color termed as blue shift.
how many moles of carbon dioxide gas occupy a volume of 81.3
What is the total amount of work required to move an electron through a potential difference of 100 volts?
Answer:2)1.6x10^-17 J
Explanation:
The ratio of hybrid cars to gasoline-powered cars in the parking lot of a local office building is 3:11. if there are 280 cars in the lot and one is to be selected at random to get the reserved parking space nearest the building, find the probability the car selected is a hybrid. express your answer as a fraction.
Answer:
The probability that it will be a hybrid is 21.4%.
Probability is the ratio of number of occurrences to total number of possible occurrences.
Given a total number of 280 cars. The number of hybrid cars is gotten by using the ratio.
Number of hybrid cars = (3/14) * 280 = 60 cars
Probability of picking a hybrid car = Number of hybrid car/total number of cars = 60 cars / 280 cars = 21.4%
Therefore the probability that it will be a hybrid is 21.4%.
Explanation:
;-
Which detail in the excerpt identifies it as fantasy? the bagginses throw extravagant parties. bilbo, a hobbit, is going to be 111. frodo is turning 33 years old. thirty-three is an important number.
The detail in the given excerpt titled The Fellowship of the Ring that identifies as a fantasy is called; Bilbo has a magic ring
What is the given excerpt fantasy:This novel titled "The Fellowship of the Ring" written by J.R.R. Tolkien has repetitive elements that define it as a fantasy novel.
These fantasy words include imagined worlds, mythical creatures and the supernatural. Since Bilbo was going to be eleventy-one 111 has these elements, then Bilbo belongs to the hobbits community which are mythical and fanatical creatures besides the age he is about to reach is unnatural even for a Hobbit.
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Answer:
B
Explanation:
2022
What is pieta?a.a sculpture of mary holding jesus’ bodyb.a sculpture of davidc.a painting of the creation of mand.a self-portrait of michelangelo please select the best answer from the choices providedabcd
Compare the boiling points of 1-pentyne and 1-octyne. compare the vapor pressure curves of 1-butene and 1-heptene. explain your reasoning.
With regards to vapor pressure curves, we can say that 1-butene has higher vapor pressures at lower temperatures than 1-heptene.
How to Interprete Vapour Pressure Curves?
With regards to boiling points, 1-pentyne has a lower boiling point than 1-octyne.
With regards to vapor pressure curves, we can say that 1-butene has higher vapor pressures at lower temperatures than 1-heptene.
Now, these supposed differences in boiling points and vapor pressures arise due to thedifferences in the chain lengths of the molecules.
Larger molecules have stronger intermolecular forces of attraction than smaller molecules. Thus, more energy is required to move larger molecules into the vapor phase from the liquid state.
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Intensive care units (icus) generally treat the sickest patients in a hospital. icus are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an icu doctor or nurse. therefore, it is important to use icus as efficiently as possible in a hospital. according to a large-scale study of elderly icu patients, the average length of stay in the icu is days (critical care medicine journal article). assume that this length of stay in the icu has an exponential distribution. do not round intermediate calculations.
a. Probability that the length of stay in the ICU is one day or less is:0.2614.
b. Probability that the length of stay in the ICU is between two and three days is:0.1426
c. Probability that the length of stay in the ICU is more than five days is:0.2198.
Probability
a. Probabilty of one day or less.
Using this formula
P(X≤1)=1-e^-ux
Since mean is 3.3 the decay parameter is:
u=1/3.3
Hence:
P(X≤1)=1-e^-1/3.3
P(X≤1)=1-e^-0.3030
P(X≤1)=1-0.7385991
P(X≤1)=0.2614
b. Probability of two and three days.
P(X≤2)=1-e^-ux
P(X≤2)=1-e^-2/3.3
P(X≤2)=1-e^-0.60606
P(X≤2)=1-0.54549589
P(X≤2)=0.45450
P(X≤3)=1-e^-ux
P(X≤3)=1-e^-3/3.3
P(X≤3)=1-e^-0.909091
P(X≤3)=1-0.402890
P(X≤3)=0.59711
Hence:
P(2≤X≤3)=0.59711-0.45450
P(2≤X≤3)=0.1426
c. Probability of more than 5 days.
P(X≤5)=e^-ux
P(X≤5)=e^-5/3.3
P(X≤5)=e^-1.515152
P(X≤5)=0.219775
P(X≤5)=0.2198 (Approximately)
Inconclusion the probability that the length of stay in the ICU is one day or less is:0.2614.
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What is the mean cost of replacing brake pads for four different vehicles at these four prices: $120, $235, $98, and $142?
The mean cost for the replacement of these brake pads for four different vehicles is equal to $148.75.
What is a mean?A mean can be defined as a terminology that is used to connote a ratio of the sum of the total number of a data set to the frequency of the data set.
How to calculate the mean cost?Mathematically, the mean cost for the replacement of these brake pads for four different vehicles would be calculated as follows:
Mean cost = [120 + 235 + 98 + 142]/4
Mean cost = 595/4
Mean cost = $148.75.
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The development of specialized tissues and organs in a multicellular organism directly results from
Lesson 30 understand probability concepts answer key
The term probability is known to be the number of times an event is expected to take place in the long run:
What is Lesson 30 understand probability about?The lesson centers around probability and this term connote the likelihood of an event occurring.
Note that an event is known to be an experiment. An outcome is regarded also as one of the possible output of the event. The lesson helps us to know more and solving questions about chances and probability.
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Which example shows an interaction between the urinary system and the circulatory system?
The main interaction between the urinary system and the circulatory system is both of the following parts of the human body work for the kidney.
The human body is the collection of many systems like the cardiovascular system for the heart, the urinary system for filtering the body, the circulating system for movement, and so on. All these functions help the body to regulate the smooth functioning of the body.
When the blood enters the kidney through arteries they go through the tiny capillaries that are seen in the urinary system. The blood entered into the kidney later moves to nephrons, where the blood is purified with the help of filters.
The waste that is obtained after the purification of the blood is then transferred to the vital substance that absorbs the bloodstream. It helps the body to manage and control the level of pressure in the blood.
Here the job of the heart is to simultaneously send the oxygenated blood all around the body and send the unwanted, discharged waste to the kidney where it helps to observe the required elements from the waste and transpose it to the urinary system.
The main work of the circulating system is to transpose the oxygenated blood to every part of the cell and provide them with sufficient nutrients.
From this system it is understandable that the similarities between circulatory and urinary system is both of the parts functions to remove waste from the body.
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when would be a good time to use a bcc rather than a cc?
Answer:
BCC has more solid uses . Here are the most common two : 1 . When you do n't want the primary recipient to know . • A good example could be when you 're having problems with an employee . When sending them an email , you can BCC your supervisor or HR in the email so that they get a copy of your correspondence . In this case , the other team members will receive it , but your fellow employee will not see that other parties have been included in the correspondence .
Explanation:
What information is not included in a company's prospectus brainly
A company's prospectus is any legal document that provides information and full details of the company.
The information in a company's prospectusThe question is incomplete, so I will list the information is a company's prospectus, instead.
The information include:
The company's management and their experienceBrief summary of the company's backgroundThe years of company's establishmentCompany name The company's principalsetc...Read more about company at:
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Answer:
the information that is not included in a company's prospectus is the company's guaranteed earning potential.
Explanation:
In a company's prospectus, its assets, net worth, and annual revenue are included in the document but not their guaranteed earning potential.
Which type of growth is best illustrated by this rabbit population?
The type of growth that is best illustrated by the rabbit population is; exponential growth.
What is the population growth?Looking the graph giving illustrated by the rabbit population seen online, it is clear that the number of individual in that population continually increase until a maximum point was reached. Thereafter, there was a slight decline in the population.
Finally, the maximum point reached on the graph is the carrying point and the value from the graph is about 0.4 million and we can say that this depicts an exponential growth model.
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If the allele for a long nose (n) is dominant to the allele for a short nose (n), what will be the relative frequency of n in a population?
The relative frquency of n in a population from the given premise of the allele is; It could be less frequent than N.
What is the relative frequency?Relative frequency is also called experimental probability and in an event , it is defined as the ratio of the number of outcomes in which a specified event occurs to the total number of trials. Though this not in a theoretical sample space but in an actual experiment.
In this question, long nose (N) is dominant to the allele for a short nose (n) and so the relative frequency will definitely be less frequent than N.
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A blood test shows clumps only in wells containing anti-a and anti-b antibodies. the rhesus test was negative. which is the correct blood type?
Answer:
AB-
Explanation:
Male and female high school students reported how many hours they worked each week in summer jobs
Answer:
The correct answer is that the males have a significantly high outlier.
Step-by-step explanation:
If you look at the box plots show the long tails t6hat signify the Q3 outlier.
classify these salts as acidic, basic, or neutral.
Which change is an unlikely result of destruction of wetlands?
Answer:
healthy fish populations
Explanation:
i just took the test and get it right