# Integral calculus: volume of a solid of revolution

1. Mar 13, 2012

### delapcsoncruz

1. The problem statement, all variables and given/known data

Find the volume of the first quadrant region bounded by x=y-y3, x=1 and y=1 that is revolved about the line x=1.

3. The attempt at a solution

dV=∏R2t

where :

t=dy
R=1-(y-y3)
=1-y+y3

so..
dV=∏(1-y+y3)2dy
dV=∏(1-2y+y2+2y3-2y4+y6)dy
V=∏∫ from 0 to 1 of (1-2y+y2+2y3-2y4+y6)dy
V=∏(y-y2+1/3(y3)+1/2(y4)-2/5(y5)+1/7(y7) from 0 to 1

V= 121∏/210 cubic units
V= 1.81 cubic units

was my solution and final answer correct?

2. Mar 13, 2012

### scurty

The setup and answer are both fine. I'm a little confused by the t, but I assume t takes the place of either dx or dy. Only thing I might suggest is to leave your answer as $\frac{121}{210} \pi$ instead of rounding, it's usually standard procedure in math courses!

3. Mar 13, 2012

### delapcsoncruz

ok i'll do that. you are right, 't' takes the place of either dx or dy, it is the thickness. thank you very much for your reply and time. appreciate it. thanks..