Calculate the area of the common interior of r = 2sin(theta) and r = 2cos(theta)

Answer 1

by symmetry,

a = 2∫[0,pi/4] 1/2 r^2 dθ
= ∫[0,pi/4] sin^2(θ) dθ
= 1/4 (2x - sin(2x)) [0,pi/4]
= 1/4(pi/2 - 1)