- #1

delapcsoncruz

- 20

- 0

## Homework Statement

Find the volume of the first quadrant region bounded by x=y-y

^{3}, x=1 and y=1 that is revolved about the line x=1.

## The Attempt at a Solution

dV=∏R

^{2}t

where :

t=dy

R=1-(y-y

^{3})

=1-y+y

^{3}

so..

dV=∏(1-y+y

^{3})

^{2}dy

dV=∏(1-2y+y

^{2}+2y

^{3}-2y

^{4}+y

^{6})dy

V=∏∫ from 0 to 1 of (1-2y+y

^{2}+2y

^{3}-2y

^{4}+y

^{6})dy

V=∏(y-y

^{2}+1/3(y

^{3})+1/2(y

^{4})-2/5(y

^{5})+1/7(y

^{7}) from 0 to 1

V= 121∏/210 cubic units

V= 1.81 cubic units

was my solution and final answer correct?