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

Calculate the volume (V) generated by the given function:

[itex]y^{2}=\frac{x^3}{2a-x}[/itex] about the line [itex]x=2a[/itex]

I suppose you have to use cylindrical shells [because it's difficult to fin [itex]y[/itex]], so:

[itex]V=2\pi(2a-x)\sqrt{\frac{x^3}{2a-x}}Δx[/itex]

now:

[itex]V=\int^{2a}_{0}2\pi(2a-x)\sqrt{\frac{x^3}{2a-x}}dx[/itex]

but I tried a million things but nothing works:

First, simplifying the integrand to this:

[itex]V=2\pi\int^{2a}_{0}\sqrt{2a-x}\sqrt{x^3}dx[/itex]

Next, I've been searching for any substitution function, but nothing works. If you have some idea that could help me I'd be grateful.

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculate the volume with a rational funtion

**Physics Forums | Science Articles, Homework Help, Discussion**