help with integration volume question please (1 Viewer)

photastic · Feb 7, 2016

Volume of the cylinder minus volume of the region bounded the function and the y-axis.

avocado111 · Feb 7, 2016

I tried that but I still got it wrong

InteGrand · Feb 7, 2016

avocado111 said:
I tried that but I still got it wrong

$\noindent Vol. of cylinder is $\pi r^2 h$, where $r=3$, $h = \ln 3$.$

$\noindent Then subtract off the volume from rotating area between $y$-axis and graph, i.e. Subtract off: $\pi \int _c ^d x^2 \text{ d}y = \pi \int _0 ^{\ln 3} e^{2y}\text{ d}y$ (as $x =e^y$). Are these the integrals you had? If so, you're only making a mistake in evaluating them, so probably a silly mistake in that case. That integral evaluates as:$

$$\begin{align*} \pi \left[ \frac{e^{2y}}{2}\right]_0 ^{\ln 3} &= \pi \left(\frac{e^{2\ln 3}}{2} -\frac{e^{0}}{2}\right) \\ &= \pi \left(\frac{9}{2} -\frac{1}{2}\right) \\ &= 4\pi. \end{align*}$

$\noindent The cylinder had volume $\pi\cdot 3^2 \cdot \ln 3 = 9\pi\cdot \ln 3$. So the final answer is $\pi \left( 9\ln 3 -4\right)$.$

help with integration volume question please (1 Viewer)

avocado111

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photastic

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avocado111

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InteGrand

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