SRL Archive - Mathematics

I have no idea how to do this problem I've been sitting here staring at my problem for 10 minutes and have made no progress




The base of a solid is bounded by y = x^3, y = 0, and x = 1. Find the volume of the solid formed by taking cross sections perpendicular to the x-axis that are semicircles..


Please help!

I've only taken beginners calc, but wolfram alpha helped me a couple of times.. Sorry I can't help much more than that.

You'll need to take the definite integral over the interval (a, b) of A(x)dx. Where A(x) is the cross-sectional areas perpendicular to the x-axis as a function of x. This is all provided that you know a formula for the region set by the cross sections. (semi-circles)

Think about the boundary points. Then integrate the volume limits. Think about where the semi-circle limits are rotated about. Do you shift the origin?

Your answer should include pi integral

Like a cone, I assume?