Area between polar curves

[rinspd]

[h=1]Find the area of the region that lies inside both curves r = A*sin(theta) and r = B*sin(theta), A > 0, B > 0?[/h]

 

[Deleted member 4993]

Find the area of the region that lies inside both curves r = A*sin(theta) and r = B*sin(theta), A > 0, B > 0?

First plot r = 1*sin(Θ) and r = 2*sin(Θ) and observe carefully at the area between those.

Then overlay r = 3*sin(Θ) on top and notice the changes (and the parameters that do not change)

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[soroban]

Hello, rinspd

Find the area of the region that lies inside both curves: .\(\displaystyle r = A\sin\theta\text{ and }\,r = B\sin\theta,\;\;A,B > 0\)

Is this a trick question?
Do they really want us to use Calculus?

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We have two circles as shown.
Their diameters are \(\displaystyle A\) and \(\displaystyle B.\)

The common area is the area of the smaller circle.