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{\bf Question}

Sketch the region enclosed by the given curves and find the volume
of the solid generated when it is revolved about the $x$-axis:

$y=x^2$, $x=1$, $y=0$.

 {\bf Answer}

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Use the disc method:

$$\int_{x=0}^{x=1} \pi(x^2)^2 \,dx = \pi \int_{x=0}^{x=1}x^4 \,dx
= \pi \left[\frac{x^5}{5} \right]_0^1 = \frac{\pi}{5}$$


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