Evaluate the integral
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Evaluate the integral

[From: ] [author: ] [Date: 11-11-05] [Hit: ]
integral [-π/3,after integration of the dr term.......
Use a double integral to find the area of the region.
The region inside the circle
(x − 2)2 + y2 = 4
and outside the circle
x2 + y2 = 4
Is the equation to evaluate integral(rcos(theta)*rsin(theta)*rdrdthe… Thanks.

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The differential area is rdrdΘ. The limits of integration for Θ and r are determined by the two circles, their intersections and/or overlaps.

Look at the units of the integrand you propose. r*r*r*dr gives the integral units of Length^4. You know that cannot be correct since the units of area are Length^2.

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I received the integral

integral [-π/3, π/3] (½ * ( 4 * cos Θ )² - 2² ) dΘ

after integration of the dr term.

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