I know how to solve this problem but I can’t figure out how to get the limits for the integral

Question

Use method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. X=5+(y-7)^2, X=14

Answer 1

Solve the equation for y.

Make a graph.

What you will have is a parabola opening to the right.

Now ask what area is it that you want to revolve about the x axis?