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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 = tan(x), for -4 â‰¤ x â‰¤ 4, about the x-axis

âˆ«(tan(x)âˆš(1 + (tan(x))^2))dx from -4 to 4

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06:05

(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 $

02:29

(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.$y=\tan ^{-1} x, \quad 0 \leqslant x \leqslant 2$

02:16

Set up an integral for the area of the surface generated by revolving the given curve about the indicated axis.y = tan(x), 0 < x < 1/4; x-axis

âˆ«(0 to 1/4) 2Ï€yâˆš(1 + (dy/dx)^2) dx

01:47

Surface area using technology 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.$y=\tan x,$ for $0 \leq x \leq \frac{\pi}{4} ;$ about the $x$ -axis

05:52

Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the x-axis. (Round your answer to three decimal places.)y = 2âˆš(x)On the definite integral from b = 2Ï€ to a = 4

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