Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a graphing utility. y=cos 2x y=0 x=0 x=pi/4

Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a graphing utility.

y = \cos 2 x

y=0
x=0

x = \frac{π}{4}

Answer 1

SchepperJ

Answered 2020-12-18 Author has 96 answers

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Answer 2

Volume of solid by disk method. Radius $= \cos (2 x)$

Area of cross section

$A (x) = π (\cos 2 x)^{2} = π (\frac{1 + \cos 4 x}{2})$

$[\cos 2 x = 2 \cos^{2} x - 1]$

$V = \int_{0}^{π / 4} A (x) d x$

$= \frac{π}{2} \int_{0}^{π / 4} (1 + \cos 4 x) d x$

$= \frac{π}{2} [x + \frac{\sin 4 x}{4}]_{0}^{π / 4}$

$= \frac{π}{2} [\frac{π}{4} + 0 - 0 - 0]$

$= \frac{π}{8}$

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a graphing utility. y=cos 2x y=0 x=0 x=pi/4

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