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- #1

- Feb 29, 2012

- 342

Find the volume of the revolution solid around the $x$ axis of the region between the curves $y=x^2 +1$ and $y=-x^2 +2x +5$ for $0 \leq x \leq 3$.

Finding the intersection of the curves yields $x=-1$ and $x=2$. Therefore, I calculated the integral

$$\pi \int_{-1}^2 [[-x^2 +2x +5]^2 - [x^2 +1]^2] \, dx$$

and found $\frac{189}{3} \pi$. However, the answer is $\frac{277}{3} \pi$. What am I missing? I am also at loss due to the fact that the question proposes the region for $0 \leq x \leq 3$ but it really occurs in $-1 \leq x \leq 2$.

All help is appreciated. Thanks!