- #1

jorgegalvan93

- 10

- 0

## Homework Statement

Find the volume of the solid generated by rotating the region bounded by the x-axis, the curve y=3x^4, and the lines x=1 and x= -1. The axis of rotation is the y-axis.

## Homework Equations

Washers method: V=∏∫ [(R)^2 - (r)^2]dr

x = (y/3)^(1/4)

## The Attempt at a Solution

So for the following problem, I used washers method to solve for the volume of the solid. R representing the outer radius, and r representing the inner radius (hole).

Because my washer is perpendicular do the y-axis, I will set my expression with respect to y… dy

I will use symmetry, so my R is 1, and r is a vertical distance so it is x, which is equal to (y/3)^(1/4)

V=∏∫ [(1)^2 - ((y/3)^(1/4))^2]dy , where the limits of integration are a = 0 and b = 3

V = 2∏∫ [(1) - √(y/3)]dy (step where problem arises)

V = 2∏[(y - 2/3(y/3)^(3/2)] from 0 to 3

V = 2∏[3 - 2/3(3/3)^(3/2)]

V = 2∏[3 - 2/3(1)]

V = 2∏[3 -(2/3)] … V = 2∏(7/3)….

V = 14∏/3

My professor said that on the second step performed, I should have done a substitution… u = y/3. I don't think that's correct though, because I would still have a 1.

Can anyone give me a hand with this problem?

Thank you!