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fakecop
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Homework Statement
Let R be the region between y=tan(x) and the x-axis from x=0 to x=pi/2. Find the volume of the solid formed when R is revolved around the y-axis.
Homework Equations
Please try to solve this problem using elementary calculus. The textbook is an elementary calculus textbook. Anything involving complex analysis or polylogarithmic functions is outside the scope of my understanding.
The Attempt at a Solution
First, we try the washer method. we have:
[itex] \int_0^\infty \pi*((\pi/2)^2-(\arctan y)^2)\,dy [/itex]
I do not know how to integrate [itex]arctan^2(y)[/itex]. Heck, the textbook didn't even explain the integration of inverse trigonometric functions, let alone [itex]arctan^2(y)[/itex]. I did find out that the integral of arctan(y) can be found via integration by parts, but I think the integral of [itex]arctan^2(y)[/itex] involves complex exponents, which is outside the scope of the textbook.
Second, we try the shell method. we have:
[itex] \int_0^{\pi/2} 2*\pi*xtanx\ dx [/itex]
And I fail to integrate x*tan(x) dx. Again, polylogarithmic functions is outisde the scope of my understanding.
Please help?
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