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Numerade Educator

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Problem 5 Easy Difficulty

(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x-axis and (ii) the y-axis.
(b) Use the numerical integration capability of a calculator to evaluate the surface areas correct to four decimal places.

$ x = y + y^3 $ , $ 0 \le y \le 1 $

Answer

a) (i)$$\quad S_{x}=\int_{0}^{1} 2 \pi y \sqrt{1+\left(1+3 y^{2}\right)^{2}} d y$$
(ii) $$\quad S_{y}=\int_{0}^{1} 2 \pi\left(y+y^{3}\right) \sqrt{1+\left(1+3 y^{2}\right)^{2}} d y$$
b) (i) $$8.5302$$
(ii) $$13.5134$$

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Video Transcript

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