Question

Find the volume of the solid obtained by rotating the region bounded by y = 35x - 7x^2 and y = 0 about the y-axis.

Answer 1

Any ideas on how to start?

Answer 2

Always draw a picture.

Answer 3

\[\pi \int\limits \limits_{0}^{5}(35x-7x^2)^{2}\]

Answer 4

What method will be the most useful here?
@awfawef that integral won't work, since you are revolving around the Y-AXIS.

Answer 5

Ok, can you tell me how and why you set it up that way?

Answer 6

You will need to use the shell/cylinder method:

Do you know how to set up an integral for this?