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WZ
Numerade Educator

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Problem 34 Hard Difficulty

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.

$ y =x^2 $ , $ x^2 + y^2 = 1 $ , $ y \ge 0 $

(a) About the x-axis
(b) About the y-axis

Answer

a) $V=\pi \int_{-0.786}^{0.786} 1-x^{2}-x^{4} d x \approx 3.544596$
b) $V \approx 1$

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Video Transcript

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