integrate integrate sqrt(x ^ 3 + 1) dx from sqrt(y) to 1 dy from 0 to 1

(a) Integrate integral cos x/sin x(1 + sin x) dx (b) Find the area bounded by the region x = 0, x = pi, y = 2 + sin x and y = x/2. (c) Find dy/dx where e^y - e^x = xy^3

Convert to a double integral in polar coordinates. Do not integrate. Where D = {(x, y) epsilon R2 |x2 + y2 4y; y x]}