# 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 = 1 + x^2#, #y = 0#, #x = 0#, #x = 2# rotated about the y-axis?

##### 1 Answer

#### Explanation:

With a problem like this, it is always a good idea to start with a graph.

We are going to rotate this shape around the

We can find our area function by stacking a bunch of circles of radius

Now that we have an area function, we just need to integrate it from the

Plug in the area function.

Move the

Solve the integral.