Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

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 $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Sky Li

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 1

Areas Between Curves

Oregon State University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

00:43

Sketch the region enclosed…

02:27

18:46

04:54

04:25

05:33

02:56

02:36

06:23

Sketch and find the area o…

Okay, this question: we need to sketch the region closed by those 22 curves and to find its area. So here is our x y plane and that, as we see, the domain is from 0 to 2 pi to a better focus on the right side to 2. Pi the first side, cotingas at looks like this. We know x, equals to pi over 2 cos x, equals to 0 and x, equals to 0 cos x equals to 1. So here is 1, so it goes like this here, it's 91 this is x, equals. Then it goes to y again. This will be all the cosine x and 2 minus cosine x, 2 minus cosine x. I i the x, equals to 0 point. This equals to 1. Okay have x, goes to pi this actually equal to 3. So this is 3. So it's like the flip, this cosine x y, this y equals 1 and then we'll get our 2 minus cosine x. This function looks like this: it reach to 3 that x equals to y. Then it goes down to okay. Then we need to find area between. Okay, so we see all the things represented by x. We determine in to use x as our integration factor, so we take the integral with respect to x and a young to x goes from 0 to 2. Pi here is just a thing inside the integral is upper curve, is minus the lower curve, so is 2 minus cos x, minus cosine x, so it will be 2 minus 2 cosine x and the anti derivative of this will be 2 x. Minus 2 sine x, evaluate x goes to 2 pi e goes to 0 point over x, equals 2 pi is equals to 4 pi sine 2 pi 0. So this term cal, so we got 4 pi and minus x equals to 0 point. We know everything here is 0, so our answer will before pi.

View More Answers From This Book

Find Another Textbook

01:00

if nth term of an AP is 5n +3 then 3rd term of the AP is a=11, b=18c, c=12d …

02:04

Almost 9 over 16 of the total water supplied to a household is used for taki…

01:56

Write the equation that is parallel to the equation y = 2x -1 and passes thr…

00:50

Find the least number that must be subtracted to 6666 so that it becomes a p…

01:48

Determine whether or not the two equations below have the same solution. In …

01:47

one disadvantage of forming a partnership is a. the number of partner is lim…

01:17

find the amount and interest on rupees 1625 at rate 12% per annum for a time…

02:01

22. In an election, there were only three candidates. 20% of the population …

03:31

what is the total cost of painting of a class room including ceiling if the …

03:40

While paying a bill, a man paid Rs 189.80 as the amount of VAT at 13%. Howmu…