- #1

tony873004

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## Homework Statement

Find the area of the region bounded by:

y=cosx, y=sin2x, 0, x=pi/2

## Homework Equations

## The Attempt at a Solution

I made a graph. I believe I'm trying to find the area I shaded.

red=cos(x), blue=sin(2x)

I need to find the intersection point so I will know the limits of my 2 integrals.

cosx = sin2x

But I don't know how to do this. There should be an infinate number of intersections, but I am only interested in the one that appears to happen around x=1/2 and the next one at what appears to be pi/2.

I can verify with my calculator that cos(pi/2) and sin(2pi/2) both equal 0, and that the right limit given by the problem is indeed the intersection, but that is not the case for the 1st intersection. How do I solve this? And what if the book gave the right limit as x=2. My method of eyeballing it and verifying my guess with the calculator would fail.

Assuming I find the intersection point, the next thing I was going to do is:

[tex]\left( {\int_0^{???} {\cos x} \,dx\, - \,\int_0^{???} {\sin 2x} \,dx} \right)\, + \,\,\left( {\int_{???}^{\pi /2} {\sin 2x\,dx} - \int_{???}^{\pi /2} {\cos x\,dx} } \right)[/tex]