evaluate-the-integrals-int-cos-3-x-sin-x-d-x

Question

Evaluate the integrals.
$\int \cos ^{3} x \sin x d x$

Ruirui Liu · Accepted Answer

Look at this institution closing you folks. Sorry. Yes. No. Okay, right. The science miners. So please and then we treed co sags and the the as unbearable. So this can&#x27;t be That&#x27;s all course.

Ruirui Liu · Answer

no sign that&#x27;s killed snow. First do some or changed in the You&#x27;re right. Well, that&#x27;s and these. So this one violence sign and we&#x27;re at the Collette. No, right. The coast a nice ready side. All these Can you sign? That&#x27;s the f mine. Just die. That&#x27;s fierce in the there, Steve Science. So we treat the science and the wearable here, so Oh, this can&#x27;t get one work for Silien. That&#x27;s worst finance or six son at six months.

Robert Daugherty · Answer

Section eight that to number 11. So we&#x27;ve got the find the anti derivative of Sign Cube co sign cubed D X. The key here is going to be organized into square perfect squares so I can write this as sine squared of x co sign cubed of X times Sign of X t X Okay, and then I can rewrite sine squared in terms of co sign squared. So this is one minus co sign squared of X times the coastline cubed of X time Sign of X d x And now, as often the case with intervals. If I can recognize a function and it&#x27;s derivative, I can make a substitution. What if you were equal to the co sign of X, then d&#x27;you is minus Sign of X T X so I can rewrite this whole intervals minus one minus co sign squared of X Times Co sign cubed of X times minus sign of ah, sign of x t X. And so this is the inner old minus. Um, one might issue squared times You cubed, do you? So this becomes minus one minus. You squared times that you cubed, do you and you multiply all of that out and you get you cubed man issue to the fifth, do you? And when you integrate this, you get minus you to the fourth over four, plus you to the 6/6, plus a constant of integration and you is equal to the co sign of X. So this is going to be the co sign to the six power of X over six, minus the co sign to the fourth power of X over four, plus a constant of integration. So the key here was to rewrite this sign cube as sine squared times sign you could alternately, you could have written this as sign Cubed X and then co sign squared of ex co side of X and then you could have rewritten coast.

Ruirui Liu · Answer

so cause they&#x27;re excuse. Yes, you can get it&#x27;s No, it&#x27;s square at times. What&#x27;s that? And, uh, this point is Morning. Morning science. You know, we right, coast any ads that you read Science. Oh, this can&#x27;t be science ex. My notes Slime square X. So these won&#x27;t treat science wearable so they can get on a horse saying, kid.

Robert Daugherty · Answer

Section eight thought to problem number nine the anti derivative over the indefinite general coastline cubed of X. So you want things to be organized into perfect squares so I can recognize that this is the integral of the co sign squared of X times of co sign of X d x, and furthermore co sign squared that is just one minus sign squared. So this is the integral one minus sine squared of x times a co sign of X dx And now I make my substitution. You is equal to the sign of X Do you is equal to co sign of X d. X. So this becomes the integral of one minus you squared, Did you? Which is just you minus you? Cubed over three, plus a constant of integration. So this becomes minus signed cubed of X over three plus sign of eggs plus a constant of integration

Amy Jiang · Answer

Okay, So in our fall in a row, we see that we have sign and co sign. We see that, um, sign has a power of three. So if we were to use use of on that you people to sign Cube the X, um, that would give us three sign of X and in times, Corbyn of X. So that seems like it makes are derivative more complicated. So why don&#x27;t we let you be equal to co sign of X and then we see that, do you? Well, that&#x27;s equal to negative. Sign of x d x. Okay, my view. Better t you sign of X Because for do you we only take one sign. So, yeah, let&#x27;s actually take you to be, um, sign of X since it has a higher power and into you. That&#x27;s the sequel to co sign of X dx. And that&#x27;s exactly what we have here. So this is the you and this would be muted of our body. So it&#x27;s your every thought. So I get you to 4/4 plus c analogy place Are you that is you is sign of X. So I have a sign of X through our 4/4 and then plus C for my solution

Problem

Evaluate the integrals. $\int \sin ^{4} 2 x \cos…

Problem 3 Easy Difficulty

Evaluate the integrals.
$\int \cos ^{3} x \sin x d x$

Answer

$\int \cos ^{3} x \sin x d x=-\frac{\cos ^{4} x}{4}+C$ where $C$ is an arbitrary constant.

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George B. Thomas Jr.

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$\int \cos ^{3} x \sin x d x=-\frac{\cos ^{4} x}{4}+C$ where $C$ is an arbitrary constant.

Thomas Calculus

Anna Marie V.

Heather Z.

Kristen K.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

George B. Thomas Jr.Thomas Calculus

Anna Marie V.

Heather Z.

Kristen K.

Joseph L.

George B. Thomas Jr.

Thomas Calculus