How do you find the area of the region bounded by the polar curves r2=cos(2θ) and r2=sin(2θ) ?

1 Answer
Nov 2, 2014

Let us look at the region.

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(Note: r2=cos2θ in purple, and r2=sin2θ in blue)

Since there two identical region, we will find a half of one region then multiply by 4. The combine area A can be found by

A=4π802sin2θ0rdrdθ

=4π80[r22]sin2θ0dθ

=2π80sin2θdθ

=2[cos2θ2]π80

=cos(π4)+cos(0)

=22+1=222


I hope that this was helpful.