Question

Integration question: http://d.pr/RTc6

Answer 1

How do you solve it?

Answer 2

how do i integrate: \[π \int\limits_{0}^{6} (y ^{2}/12 +1)^{2} dy\]

Answer 3

Rotate the rectangle first, then rotate the parabola itself, find individual volumes then subtract the volume of the solid generated by the parabola from the solid generated by the rectangle

Answer 4

and for that integral, just multiply it out.

Answer 5

And then integrate term by term that will make your life easy.

Answer 6

actually finding the vol of the solid generated by the rectangle is easy.

Answer 7

I've been taught to integrate like this when the limits are on the y axis: \[\int\limits_{a}^{b} π x ^{2} dy\]

Answer 8

It generates a cylinder with radius 6 and height 4

Answer 9

Yea but you don't really have to do that for the solid generated by the rectangle. If you rotate it around it generates a cylinder.

Answer 10

What rectangle are you referring to?

Answer 11

Imagine a line passing through (4,6) and (4,0)

Answer 12

that will form a rectangle right? with the line y = 6, x = 4, and x and y axes

Answer 13

yes, i see. But what do you after that?

Answer 14

you can do this with disk or shell method. Do you know both?

Answer 15

So find the volume of the solid generated by that rectangle - it will be a cylinder

Answer 16

I haven't heard of the 'disk' or 'shell' method?

Answer 17

What do i do after working out the vol. of solid rectangle?

Answer 18

Find the volume generated by revolving the following area and then subtract it from the vol of the cylinder.