Question

For Problems 17 & 18, find the area of the surface generated by rotating the given curve about the given axis. 17. $f(x) = \sqrt{4 - x^2}$; rotated about the x-axis. 16$\pi$ 18. $f(x) = x^2$, $1 \le x \le 2$; rotated about the y-axis. $\frac{4\pi}{3} \left( \left(\frac{17}{4}\right)^{3/2} - \left(\frac{5}{4}\right)^{3/2} \right)$

          For Problems 17 & 18, find the area of the surface generated by rotating the given curve about the given axis.
17. $f(x) = \sqrt{4 - x^2}$; rotated about the x-axis.
16$\pi$
18. $f(x) = x^2$, $1 \le x \le 2$; rotated about the y-axis.
$\frac{4\pi}{3} \left( \left(\frac{17}{4}\right)^{3/2} - \left(\frac{5}{4}\right)^{3/2} \right)$

For Problems 17 18, find the area of the surface generated by rotating the given curve about the given axis.
17. f(x) = √(4 - x^2); rotated about the x-axis.
16π
18. f(x) = x^2, 1 ≤ x ≤ 2; rotated about the y-axis.
(4π)/(3)( ((17)/(4))^3/2 - ((5)/(4))^3/2)

Added by Suzanne H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Oswaldo Jiménez

09/03/2023

Step 1

The formula for the surface area of a solid of revolution generated by rotating a curve $y = f(x)$ around the x-axis from $x = a$ to $x = b$ is given by: \[ A = 2\pi \int_{a}^{b} f(x) \sqrt{1 + (f'(x))^2} dx \] Show more…

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How can I find questions 17 and 18? For Problems 17 & 18, find the area of the surface generated by rotating the given curve about the given axis 17. f(x) = 4- x2 ; rotated about the x-axis. 16TT 18.f (x)=x2, 1x2 ; rotated about the y-axis 4-)