What is the surface area of the solid created by revolving #f(x) = x^2+e^x , x in [2,4]# around the x axis?
First, take a look at the graph
I've drawn vertical lines at the endpoints to show where the solid would revolve around the
The formula for find the volume of a shape like this is
In this case, you can plug in all the values and find the integral in a straight forward fashion.