Is this what you're looking for?.
This gives the area from 0 to Pi. In other words, the smaller portion above the 'x-axis', so to speak.
I just integrated from 0 to Pi. You can do it from 0 to Pi/2 and multiply by 2 as well to get the same thing.
The problem said area above the polar axis. It starts at what we can say is the positive x-axis and turns counterclockwise to Pi so that it encompasses all the area above the polar axis. After you pass Pi(180 degrees) you get below it. I shaded the wanted region, but it did not appear when I saved it to post. Sorry 'bout that.
Did you make a sketch?
This is a cardioid . . .Find the area of the interior of (above the polar axis)Code:| ..*.. | ..*.. *:::::::* | *:::::::* - - * - - - - - * - - - - - * - - * | * | * | * * | * * | * | * | * * | * * | * * | * * * * |
We can find the area from to . . . and double.
So we have:.
I get: .