Question

Consider the region bounded by y = x^2 and the line y = 25. Find the exact volume of the solid obtained by rotating the region about the x-axis

Answer 1

i tried using the disk method :\[\pi(x^2)^2 \] and integrating that from 0 to 5 but not luck

Answer 2

Problem isit's not x^2, that's actually the opposite of what you want. If you chose x^2 as your radius, you would get the region bounded by x^2 and the x-axis, but not theregion bounded by x^2 and y = 25. You actually need 25-x^2 to be your radius to get the correct bounded region.