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

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.