renegade05
Full Member
- Joined
- Sep 10, 2010
- Messages
- 260
for the region R, determine the volume of the solid generated when R is revolved about the y-axis.
R is bounded by y=1-x^3, the x-axis, and the y axis
So...
\(\displaystyle x=(1-y)^{\frac{1}{3}}\)
\(\displaystyle \pi\int^1_0 (1-y)^{\frac{2}{3}}\,dy\)
\(\displaystyle =\pi\left[\frac{3(1-1)^{\frac{5}{3}}}{5}-\frac{3(1-0)^{\frac{5}{3}}}{5}\right]=\frac{-3\pi}{5}\)
but the book has
\(\displaystyle \frac{3\pi}{5}\)
as the answer. why ?
R is bounded by y=1-x^3, the x-axis, and the y axis
So...
\(\displaystyle x=(1-y)^{\frac{1}{3}}\)
\(\displaystyle \pi\int^1_0 (1-y)^{\frac{2}{3}}\,dy\)
\(\displaystyle =\pi\left[\frac{3(1-1)^{\frac{5}{3}}}{5}-\frac{3(1-0)^{\frac{5}{3}}}{5}\right]=\frac{-3\pi}{5}\)
but the book has
\(\displaystyle \frac{3\pi}{5}\)
as the answer. why ?
