Calculus Help

Question

The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(e^x) is rotated about the x-axis. What is the volume of the generated solid?

Answer 1

V=π∫₀^ln(π)sin(e^x))²dx=0.79..

Another way to find the Volume is to look at x a function of y. Then x=ln(arcsin(y)) 0<=y<=1 and you have to  keep in mind that revolution around x (dependent) variable.