Integral calculus: volume of a solid of revolution

[delapcsoncruz]

Homework Statement

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.

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?

 

[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!

 

[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..