Find the area of the region bounded by the curves y = sin^-1(x/4) , y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative.

Answer 1

Note that x=4siny and you want the area "above" the curve
a = ∫[0,pi/2] 4-4siny dy = 4y+4cosy [0,pi/2] = 2pi-4