How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y=x^(1/2)#, #y=0#, and #x=4# rotated about the x axis?
1 Answer
This solid to-be-revolved looks like:
graph{(y - sqrtx)(y)sqrt(4-(x-0))/sqrt(4-(x-0)) <= 0 [-5, 5, 0, 5]}
If you want to do it with the shell method, convert your functions to their inverses.
You get:
Now your domain is your range and your interval is
graph{(y - x^2)sqrt(4-(y-0))/sqrt(4-(y-0)) >= 0 [0, 8, -1, 5]}
Note: if you evaluated this using