What is the area of the region in the first quadrant bounded by the x-axis, the line , and the circles and ?

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- Aug 9th 2012, 05:35 PMMrdavid445Area of Region
What is the area of the region in the first quadrant bounded by the x-axis, the line , and the circles and ?

- Aug 9th 2012, 08:01 PMGJARe: Area of Region
Hi, Mrdavid445.

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?

Good luck! - Aug 10th 2012, 12:01 AMearbothRe: Area of Region
Since you posted your question in the Geometry forum you probably wanted to use a more geometrical way to solve the problem(?).

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.