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 $R$ about the $x$ axis.
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Answer

$V = π {[\frac{1}{2} x^{2}]}_{0}^{4}$

Steps

Step 1 ： $V = π \int_{0}^{4} (\sqrt{x})^{2} d x$

Step 2 ： $V = π \int_{0}^{4} x d x$

Step 3 ： $V = π {[\frac{1}{2} x^{2}]}_{0}^{4}$

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