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(A) The volume $V$ of a solid generated by rotating a curve $y = f(x)$ about the $x$-axis between $x = a$ and $x = b$ is given by the formula: $V = \i

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(A) The volume $V$ of a solid generated by rotating a curve $y = f(x)$ about the $x$-axis between $x = a$ and $x = b$ is given by the formula: $V = \int_{a}^{b} \pi y^{2} dx$. Given the curve $y^{2} = 4x$ and the limits $x = 4$ to $x = 5$. Substituting the values into the formula: $V = \int_{4}^{5} \pi (4x) dx$ $V = 4\pi \int_{4}^{5} x dx$ $V = 4\pi \left[ \frac{x^{2}}{2} \right]_{4}^{5}$ $V = 2\pi [x^{2}]_{4}^{5}$ $V = 2\pi (5^{2} - 4^{2})$ $V = 2\pi (25 - 16)$ $V = 2\pi (9) = 18\pi$ cubic units.

The volume of the solid formed by rotating the area enclosed between the curve $y^{2}=4x$, $x=4$, and $x=5$ about the $x$-axis is (in cubic units): (in $\pi$)

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