Finding the total area of the shaded region.

[november1992]

Homework Statement

http://img545.imageshack.us/img545/6260/hardproblem.png

Homework Equations

1. First I solved for y
2. I put it in the form f(x)-(g(x)
3. Then I integrated

The Attempt at a Solution

The answer in my book says it is ∏/2.

I don't think I'm integrating right. I end up with this towards the end

http://img15.imageshack.us/img15/2431/hardproblem3rdstep.png

 

[Mark44]

Homework Statement

http://img545.imageshack.us/img545/6260/hardproblem.png

What shaded region? There is nothing shaded. What is the verbal description of the region?

Homework Equations

1. First I solved for y
2. I put it in the form f(x)-(g(x)
3. Then I integrated

The Attempt at a Solution

The answer in my book says it is ∏/2.

I don't think I'm integrating right. I end up with this towards the end

http://img15.imageshack.us/img15/2431/hardproblem3rdstep.png

No, that is incorrect. To confirm this fact, differentiate your result. If you don't get the original integrand, that's a clue that you're on the wrong track.

There's a trig half-angle identity you can use to integrate that squared cosine.