Question
The region under the curve $y=\tan ^{2} x$ from 0 to $\pi / 4$ is rotated about the $x$ -axis. Find the volume of the resulting solid.
Step 1
The formula for the volume of a solid of revolution about the x-axis is given by $V=\pi\int_{a}^{b} [f(x)]^{2} dx$. Here, $f(x) = \tan^{2}(x)$ and the limits of integration are from 0 to $\pi/4$. Show more…
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$\begin{array}{l}{\text { The region under the curve } y=\sin ^{2} x \text { from } 0 \text { to } \pi \text { is rotated }} \\ {\text { about the } x \text { -axis. Find the volume of the resulting solid. }}\end{array}$
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