Question

Integration (volume)

Answer 1

What is the volume in terms of pi?

Answer 2

Is it really volume, though?

Answer 3

Did you mean area?

Answer 4

Volume. Rotate Y axis

Answer 5

Oh yes... silly me :D

Answer 6

Then perhaps we should integrate with respect to y...

Answer 7

Can i use shell method?

Answer 8

Shell? Sure. But I prefer disks.

Answer 9

Personal preference, really, but I'm just not comfy with shells. The tricky part is setting up what to integrate.

Answer 10

So whats the equation?

Answer 11

It is so complicated to use disc method

Answer 12

why not make quick sketches first, one of them showing a representative shell, the other showing a representative disk? Then consider again whether to use shells or disks. You could use either. In fact, I'd suggest you do this problem both ways and then decide for yourself which is easier for you in THIS particular situation.

Answer 13

To me the better method is obvious. Sketches such as ganeshie8's may help you to understand why.

Answer 14

h=2 r=root2

Answer 15

I got the answer now

Answer 16

\[V=\frac{ 1 }{ 3 }\pi r ^{2}h+\int\limits_{\sqrt{2}}^{2}\pi (4-y ^{2})dy\]

Answer 17

Haha i just think it is easier to do it in this way

Answer 18

Anyway thanks