5

10. (SPts_ )Evaluate the iterated integral: 3 6 & 3 dr d0 dz...

Question

10. (SPts_ )Evaluate the iterated integral: 3 6 & 3 dr d0 dz

10. (SPts_ )Evaluate the iterated integral: 3 6 & 3 dr d0 dz



Answers

Evaluate the integral by making the given substitution. $\int \cos ^{3} \theta \sin \theta d \theta, \quad u=\cos \theta$

I can write the given integration edge integration 0 to 1 be because as cube from zero to Esquire Bs simplifying it further I can I've 0 to 1 integration as it squad because as cube minus zero ds on further solving I can write Evaluate you go to one as the square multiplication cause Ask you bs on further going now latest take ask you is equal to you So three years is square ds will become the you so access square D s is equal to one by three Do you now? When I extend to zero, you tend to zero So when ash tends to one, you don't tend to one. Therefore the question can be written edged integration of 0 to 1 cause you BU by three on further solving I can write devaluate one by three integration of 0 to 1 because you d which is equal to one by three multiplication Sign you from 0 to 1 which is equal to one by three Sign one minus zero On further solving I get the value edge one by three Sign one This is our answer

Okay, here we go. Uh, we'll start off since s has been held. Constant. This just become a T co sign s cubed from T equals zero to t equals s squared. Okay. And that becomes s squared. Co sign of this. Killed minus zero. Won't zero co sign as a cue? Yes. OK, so we just have this now. Sierra one s squared co sign of s cubed ts, and we're gonna make use of this form the, um Let's see the integral of co sign of you, d you. It's going to be minus sign of you. And we almost have that here. But are you in this case is yes, that's cubed. So do you would be the three s squared ts. Now we have that, except for the three. So you go ahead and put a three in here and put a 1/3 outfront that fixes it. So now we have this exact form and we can then just go ahead. Integrate will have 1/3 sign that's cubed from 0 to 1. It'll be 1/3 sign of one killed minus a sign of zero killed, which will just be in a sign of 1/3

So here we are given a double integral. So it's important to remember when we're doing a double integral or triple integral integration, we're basically looking for uh we're only or assuming that the non and the variable not being integrated, the parts of that are just going to be a constant. So since we're integrating for the variable T. We can bring out the coastline S cube out of the integral expression. Since this would just be a constant. So this would just be the integral of one would just be T in this case. And once we substitute for S squared this would be the integral from 0 to 1 of the square co sign of X cubed Diaz. So now we can use U substitution where we take s cubed as you and then we take d'you equivalent to three S squared. The uh T. S. And this would be one third would be S equals zero. S equals one of co sign of you to you. So that uh the integral, of course you would just be sign of you. So this would be one third sign of S cute. From zero to once a sign of zero is just zero Sign of a sign of one would be equivalent. So this would just be 1/3 sign of one. And this gives our final answer

In this problem. First time integrating the given value with respect to X, considering via the content so I can write the express and has 0 to 1. He took the power White Cube Access Choir by two 02 y divide, simplifying it further. I cannot evaluate one by two, 0 to 1. Why squad it to the power? Why cube dy now let us take why Cuba is equal to T. Then three wise square dy will become DT going forward and solving it. For that I can write y squared dy is equal to D 80 by three when why is it called to zero? Is equal to zero when y is equal to one he is equal to one cube is equal to one now going forward and simplifying it for the so I can write the expression integration of 0 to 1 Why is required it to the power y cube Divide multiplication one by two on solving it I can ride evaluate one by six Integration of 0 to 1 It is the power t d t on further solving. I can ride evaluate one by six he to the poverty from 0 to 1. On further simplification, I get the value of one by six e to the power one minus e to the power he to the power one minus one, which is equal to one by six. E minus one. This is our final answer.


Similar Solved Questions

5 answers
Write IUPAC name for cach of the following:
Write IUPAC name for cach of the following:...
5 answers
Compound 5, CsHtOz4CoO33007ooo1600
Compound 5, CsHtOz 4CoO 3300 7ooo 1600...
5 answers
Of the hypothesis Ho: / = 150 versus Hj: p 150 was 40. A test performed The P-value was 0.28. Fill in the blank: If u = 150, then the probability of observing a test statistic as extreme as Or more extreme than the one actually observed is
of the hypothesis Ho: / = 150 versus Hj: p 150 was 40. A test performed The P-value was 0.28. Fill in the blank: If u = 150, then the probability of observing a test statistic as extreme as Or more extreme than the one actually observed is...
5 answers
(a) Ji 8i two Ji W such that Awll 12 Find ~Zu+4v|l:3
(a) Ji 8i two Ji W such that Awll 1 2 Find ~Zu+4v|l: 3...
5 answers
3 M 3 3 8 H 2 8 88 1 2la 2 w [ 5 2| 2 8 3 2 7][ 33 9 1 I E 3
3 M 3 3 8 H 2 8 88 1 2la 2 w [ 5 2| 2 8 3 2 7] [ 33 9 1 I E 3...
1 answers
The process x(t) is WSS and normal with Elx(t)}=0 &nd R(r) =4e-Zl_ (a) Find P{x(t) < 3}. (b) Find E{lx(t + 1) - x(t 1)P}
The process x(t) is WSS and normal with Elx(t)}=0 &nd R(r) =4e-Zl_ (a) Find P{x(t) < 3}. (b) Find E{lx(t + 1) - x(t 1)P}...
5 answers
The value for Kwis cqual to the [H;O' (aQIIOH (9]changes depending on the pHshows that adding OH (aq) inereases the [H;O' (aq)]10-14 molll shows that the [OH (aq)] can never be less than [.00
The value for Kw is cqual to the [H;O' (aQIIOH (9] changes depending on the pH shows that adding OH (aq) inereases the [H;O' (aq)] 10-14 molll shows that the [OH (aq)] can never be less than [.00...
5 answers
Question Complction StatusQUESTIONand then convert that cm measurement into inches and meters Measure the thick bar incm (254 cm inch; 100 cm Im) Show your work Number of inches: Number of meters: For the toolbar,press ALT F1O (PC)or ALT FN F1O (Mic) Paragraph Anal 1apxtClick Savc and Submitto savesubmit; Click Save All Answers to sar? all ansuersSave A An
Question Complction Status QUESTION and then convert that cm measurement into inches and meters Measure the thick bar incm (254 cm inch; 100 cm Im) Show your work Number of inches: Number of meters: For the toolbar,press ALT F1O (PC)or ALT FN F1O (Mic) Paragraph Anal 1apx t Click Savc and Submitto ...
5 answers
The products of reaction of alcoholic silver nitrite with ethyl bromide are(a) ethane(b) ethene(c) nitroethane(d) ethyl alcohol(e) ethyl nitrite
The products of reaction of alcoholic silver nitrite with ethyl bromide are(a) ethane (b) ethene (c) nitroethane (d) ethyl alcohol (e) ethyl nitrite...
5 answers
Moving to the next question prevents changes to this answer.Question 1How many promising drug compounds discovered never make it to market? @I0005C00"@)10,0o015,000Moving t0 the next questian prevents changes to this answer
Moving to the next question prevents changes to this answer. Question 1 How many promising drug compounds discovered never make it to market? @I000 5C00" @)10,0o0 15,000 Moving t0 the next questian prevents changes to this answer...
5 answers
Gayle runs at a speed of 4.15 m/s and dives on a sled, initiallyat rest on the top of a frictionless snow-covered hill. After shehas descended a vertical distance of 5.00 m, her brother, who isinitially at rest, hops on her back and together they continue downthe hill. What is their speed at the bottom of the hill if thetotal vertical drop is 15.0 m? Gayle's mass is 47.5 kg, the sledhas a mass of 5.05 kg and her brother has a mass of 30.0 kg.m/s
Gayle runs at a speed of 4.15 m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the...
5 answers
Table 3-- Calculations for the Determination of an Equilibrium ConstantInitial Concentrations [Fe"t] [SCN ]Equllibrium Concentrations (Fe3] (SCN-] (FeSCN?-)KeqAverage value for Keq 5
Table 3-- Calculations for the Determination of an Equilibrium Constant Initial Concentrations [Fe"t] [SCN ] Equllibrium Concentrations (Fe3] (SCN-] (FeSCN?-) Keq Average value for Keq 5...
5 answers
3 9 Find the general term of the sequence: 1, 2,. 2 53+n3n b) 2n3"3n n +2nn +2
3 9 Find the general term of the sequence: 1, 2,. 2 5 3+n 3n b) 2n 3" 3n n +2 n n +2...
5 answers
Pel' Question Eight According to the USDA the daily calorics consumption of adults, nges 20 to JS years old; [s 2680 With standard deviation of 80 . Assuming the amount of calories consumption for ndults nonnally distnbuled, 10 adults Wen ~clected mndom; what the prohability that the avcrave enlories consumption of thcm mon han 2700 culories per duy"
Pel' Question Eight According to the USDA the daily calorics consumption of adults, nges 20 to JS years old; [s 2680 With standard deviation of 80 . Assuming the amount of calories consumption for ndults nonnally distnbuled, 10 adults Wen ~clected mndom; what the prohability that the avcrave e...
5 answers
We estimate tne following regression model : SCORE 698.9 - 2.28 CLASS_SIZE ERROR Provide an interpretation of tne estimate of the intercept coefficient
We estimate tne following regression model : SCORE 698.9 - 2.28 CLASS_SIZE ERROR Provide an interpretation of tne estimate of the intercept coefficient...

-- 0.021757--