alexcarrasco8676 alexcarrasco8676
  • 08-08-2017
  • Mathematics
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Calculate the area of the circle r = 6 sin ? as an integral in polar coordinates. be careful to choose the correct limits of integration

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jbmow
jbmow jbmow
  • 08-08-2017
r2=x2+y2 and sin(θ)=y/r

Therefore,

r=SQRT(x2+y2)

and 6sin(θ)=6yr

The original equation turns into:

SQRT(x2+y2)=6y/r

or  x2+y2=6y

Completing the square turns this into x2+(y−3)^2=9

, a circle centered at (0,3) with a radius of 3

The area of that circle is 9π


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