Calculus in Polar coordinates

Question

Find the area of the region that lies inside the first curve and outside the second curve.

r = 5 − 5 sin(𝜃),    r = 5

Answer 1

Plot the curves in question.

The area in question is symmetric about the y-axis.

Integrate the cardioid from pi to 3 pi/2

Then subtract 6.25 pi (the area of the quarter circle)

Double that difference.

Remember the integrand for the area of the cardioid is .5(5-5 sin θ)² dθ