Need help with region rotated about the x-axis question (1 Viewer)

BlueGas · Mar 22, 2015

I need help with question b) in the picture below.

InteGrand · Mar 22, 2015

BlueGas said:
I need help with question b) in the picture below.

$V=\pi \int_{0}^{1}\left ( \frac{3}{(x+2)^2} \right )^2\text{ d}x=\pi \int_{0}^{1}\frac{9}{(x+2)^4}\text{ d}x$

$= 9\pi \int_{0}^{1}(x+2)^{-4}\text{ d}x$ (now we just use power rule to integrate)

$= \frac{9\pi}{-4+1}\left [ (x+2)^{-4+1} \right ]^1 _0$

$=-3\pi\left [3^{-3}-2^{-3}\right ]$

$=\frac{19}{72}\pi \text{ cubic units}$ (simplifying).

Need help with region rotated about the x-axis question (1 Viewer)

BlueGas

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InteGrand

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