From the diagram below, it looks like
Which will come out to be .
Here's a cool calc problem you may wish to tackle. Perhaps you've seen it before.
"A wedge is cut from a cylinder of radius r by two planes, one perpendicular to the axis of the cylinder and the other making an angle @ with the first. Find the volume of the wegde by slicing perpendicular to the y-axis".
Then find the volume by slicing perpendicular to the x-axis.
Here's a diagram to help. I used @ instead of theta because I used paint to construct the diagram.
Good Jane. That's certainly it. It appears you done it perp. to the x-axis.
Here's the perp. to the y-axis version:
Let the height of the triangle be h
Then we have
The area of the triangle is
And our integral is: