AP Calculus: Area bound by curves.

Question

Find the area of the region bounded by the curves y = sin^-1(x/2), y = 0, and x = 2 obtained by integrating with respect to y. Please include the definite integral and the antiderivative.

Answer 1

y=sin^-1(x/2), y=0, x=2

x=2sin(y), x=2, y=0.  2sin(y)=2 --> sin(y)=1, y=π/2. So 0≤y≤π/2.

Area=∫₀^π/2(2-2sin(y))dy=π-2.