(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the area of the region bounded by:

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

2. Relevant equations

3. 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]

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Area between curves

**Physics Forums | Science Articles, Homework Help, Discussion**