Question

Help please! I need to find the volume of this object.

Answer 1

So we now the equation for the parabola is -\[y=3x^2+3\] so we need to solve for x\[x=\sqrt(\frac{ y+3 }{ 3 })\]

Answer 2

We know that \[Area = g(y)-f(y)\]

Answer 3

So lets divide it in half at x=3 so we just need to multiply by 3 to get the whole length .
\[A=2(3-\sqrt( \frac{ y+3 }{ 3})\]

Answer 4

@Loser66 Does this look correct so far?

Answer 5

I would like to see the problem.

Answer 6

There it is

Answer 7

Ok, so the area should be (2(3-x))^2 , right?

Answer 8

And you replace x = sqrt (y+3)/3

Answer 9

Ohhh, that is how you do it.

Answer 10

Yes that makes so much more sense

Answer 11

:)

Answer 12

So then we take the integral from 0 to 3 of all that. Let me just write that down quick.

Answer 13

Alright so we have