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Question

Consider the following curves on the given intervals. a. Write the integral that gives the area of the surface generated when the curve is revolved about the given axis. b. Use a calculator or software to approximate the surface area. $y=(2 x+3)^{2}$, for $0 \leq x \leq 1$; about the y-axis

Solution

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Answered 1 year ago

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1 of 3Let $x = g(y)$ be greater of equal to $0$ with continuous first derivative on interval $[c, d]$. The area of the surface generated when the the graph of $g$ on the interval $[c, d]$ is revolved about the $y$-axis is

$S = \int_c^d 2\pi g(y) \sqrt{1 + g'(y)^2 } \,dy$

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