Find the volume of the solid obtained by rotating the region-2

phillyolly
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Homework Statement


Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. About x axis.

y=sqrt(25-x2)
y=0
x=2
x=4

Homework Equations





The Attempt at a Solution


I drew a graph, region and solid. Please help me out with the disk.
Jump start for any solution, please?
 

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I posted this in your other thread, here's the link: https://www.physicsforums.com/showthread.php?t=418382"

This figure should give you some intuition on visualizing the disks.

I don't really understand where your confusion lies, so if there is any please specify where and why.
 
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Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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