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Numerade Educator

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Problem 6 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.

$ y = \tan^{-1} x $ , $ 0 \le x \le 2 $

Answer

a)(i) $$\quad S_{x}=\int_{0}^{2} 2 \pi \arctan x \sqrt{1+\left(\frac{1}{1+x^{2}}\right)^{2}} d x$$
(ii) $$\quad S_{y}=\int_{0}^{2} 2 \pi x \sqrt{1+\left(\frac{1}{1+x^{2}}\right)^{2}} d x$$
b) (i) $$9.7956$$
(ii) $$13.7209$$

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Video Transcript

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