Question

Is the answer 0 for this problem? Sketch region enclosed by the given curves and find its area. y=cosx, y=2-cosx, 0 12 years ago

Answer 1

http://www.wolframalpha.com/input/?i=y%3Dcosx%3B+y%3D2-cosx

Here is a graph of the two

Answer 2

how can i find its area?

Answer 3

Are you taking trig or calculus?

Answer 4

calculus

Answer 5

You must find the definite integral of the function cos(x) first. What is the evaluation of the following?
$$\int_0^{2\pi} \cos x \, \mathrm{d} x$$

Answer 6

@bloopman is it 0?

Answer 7

Correct.

Answer 8

Now, once you've graphed the functions, you see you just have to subtract the area under the curve of cos(x) from 2 - cos(x); however, since the indef. integral over cos(x) is 0, we just take the definite integral of 2-cos(x) on the boundary [0, 2pi]. That is:
$$\int_0^{2\pi} 2 - \cos x \, \mathrm{d} x$$

Answer 9

i got 0 is it right?