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How do you find the volume of the region bounded by $y = {(x)}^{\frac{1}{2}}$ $y = (x)^(1/2)$ ; $y = 0$ $y=0$ and $x = 4$ $x = 4$ rotated about the x-axis?

1 Answer

Aug 6, 2015

$8 π$ $8 pi$

Explanation:

$y = x^{\frac{1}{2}}$ $y = x^(1/2)$
$V = π \int_{0}^{4} y^{2} d x = \frac{π}{2} {[x^{2}]}_{0}^{2} = 8 π$ $V = pi int_0^4y^2dx = pi/2[x^2]_0^4 = 8pi$

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