(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the volume of the solid which is obtained by revolving the discs [tex](x - 1)^2 + y^2 \le 1[/tex]

3. The attempt at a solution

I say using cylinders would be easiest so,

[tex]\int_a^b{2\pi r(x)h(x) dx} = \int_0^2{2\pi x\sqrt{1-(x-1)^2} dx}[/tex]

Any hints on how to get started with this integral?

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1. The problem statement, all variables and given/known data

Find the arclength of the curve [itex]y = e^x[/itex] with [itex]0 \le x \le ln 2[/itex]

3. The attempt at a solution

[tex]y' =e^x[/tex]

so I need to solve

[tex]\int_a^b{\sqrt{1+(y')^2}dx} = \int_0^{ln 2}{\sqrt{1+e^{2x}}dx}[/tex]

Any hints?

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# Calc II

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