# Double integral-semi circle

• aspiring_gal

#### aspiring_gal

if the quest is like this:

Show that double integral over R ( r2 sin(theta)) dr d(theta), where R is the region bounded by the semicircle r=2acos(theta), ABOVE THE INITIAL LINE...

? theta varies from...?

finally after 1st integration I got the value as
integral of___ to ___ -[(8a^3)/3] * [((cos^4)theta]...

Am I right till this step?...if not, please correct!

AG if the quest is like this:

Show that double integral over R ( r2 sin(theta)) dr d(theta), where R is the region bounded by the semicircle r=2acos(theta), ABOVE THE INITIAL LINE...
Show that the double integral [/b]what[/b]? The predicate of your sentence is missing! Do you just mean evaluate the double integral?

? theta varies from...?

finally after 1st integration I got the value as
integral of___ to ___ -[(8a^3)/3] * [((cos^4)theta]...

Am I right till this step?...if not, please correct!

AG That figure is the circle with center at (a, 0) and radius a. The entire circle is swept out as $\theta$ goes from 0 to $2\pi$. Since r= 2a(cos(0))= 2a, the initial point is (2a, 0) and the "initial line" is the x-axis. "above the initial line" is the upper half of the circle which is swept out as $\theta$ goes from 0 to $\pi$.
As for what you have done already, since there is a "$sin(\theta)$" in your integrand, I don't see how integrating with respect to r could get rid of that!