Problem

Question 21 (5.2 points)
Let \( R \) be the region in the first quadrant bounded by the \( x \)-axis, the line \( x=4 \), and \( y=\sqrt{x} \). Compute the volume of the solid obtained by revolving \( \mathrm{R} \) about the \( \mathrm{x} \) axis.
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Answer

\( V = \pi \left[\frac{1}{2}x^2\right]_{0}^{4} \)

Steps

Step 1 ：\( V = \pi \int_{0}^{4} (\sqrt{x})^2 dx \)

Step 2 ：\( V = \pi \int_{0}^{4} x dx \)

Step 3 ：\( V = \pi \left[\frac{1}{2}x^2\right]_{0}^{4} \)

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