What is the area of the region in the first quadrant bounded by the x-axis, the line , and the circles and ?
The area of a region R in the plane is given by
where dA is the area element. Since the region we're interested in is a portion of an annular region, it's best to use the polar form for dA, which is
What remains are to determine the limits of integration and then compute the double integral.
Does this get everything going in the right direction?
1. The area in question is the difference of 2 sectors of 2 concentric circles:
Draw a sketch!
2. The area a is calculated by:
Plug in the known values.