# More volume problems integration

• Feb 19th 2013, 09:55 AM
togo
More volume problems integration
Am I on the right path for this first problem?
Problem 1:
Use Shell method, rotate about X axis
Curve: x = 4y - y^2 - 3
solving for y
x + 3 = 4y - y^2
x + 3 + y^2 = 4y
(x + 3 + y^2)/4 = y

Is this correct so far?

Problem 2:
use Disks, rotate about Y axis
Curve: y = x^1/3
formula for disks: pix^2 dy
so we must solve for x
I seem to be at a loss for how to get something = x
do we multiply both sides by a certain exponent to get an exponent of x^1?

any tips, thanks
• Feb 19th 2013, 12:43 PM
HallsofIvy
Re: More volume problems integration
Quote:

Originally Posted by togo
Am I on the right path for this first problem?
Problem 1:
Use Shell method, rotate about X axis
Curve: x = 4y - y^2 - 3
solving for y
x + 3 = 4y - y^2
x + 3 + y^2 = 4y
(x + 3 + y^2)/4 = y

Is this correct so far?

No, it isn't, because you haven't yet "solved for y" with that "y^2" on the left.

Quote:

Problem 2:
use Disks, rotate about Y axis
Curve: y = x^1/3
formula for disks: pix^2 dy
so we must solve for x
I seem to be at a loss for how to get something = x
do we multiply both sides by a certain exponent to get an exponent of x^1?
A 1/3 power is the cube root, isn't it? And the opposite of the cube root is cubing.

Quote:

any tips, thanks