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SL
Numerade Educator

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Problem 16 Easy Difficulty

Sketch the region enclosed by the given curves and find its area.

$ y = \cos x $ , $ y = 2 - \cos x $ , $ 0 \le x \le 2\pi $

Answer

4$\pi$

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Video Transcript

Okay. This question. We need to sketch the region closed by those two. Took to curves in a fine is area. So here is some x y plain, uh, And as we see the domains from zero to two pi or better focus On the right side, there are two pipes. The first size ko. Thanks. Because I actually look like that, huh? They know, uh, ex yuko's to pie or two Cossacks equal to zero on the ax equals zero Kozak. Seacoast one. Here's one goes like this. You're a right one. This is X equals pi. It goes to why, Yeah, OK, but this will be all the co Xanax. And to Linus go sonics. Um, Linus goes on X and X uh, close to zero. This ecosystem one okay of the ex coast to pie. This actually counted three. So Jim uses three. Hey, it's like they flip this costar X life is why you coast war and we'LL get our two minus co psychics So this functional look like tears. Hey, the rich to three. The ax he caused by then it goes down to what? Okay, then we need to find area in between. Okay? So we see all the things represented. Backpacks. We determine into use X as our our integration factor. So we take them to grow with respect acts I can have. You know, X goes from zero to two. By here is the thing inside Integral is upper Curve is minus the lower curb. So is two minus Cozaar Max minus Cossacks. There will be two minus to Cosette and Auntie do give office will be on to X miners. Two sidekicks. You added it at access codes to to pi. And he goes to zero over X equals to privacy close to four pi. Um, signed two point zero. So this term skull. So we got four pi and minus X equals zero. We know everything. There is zero. So our answer all before pie.