# Integral of r^2 times square root of 4r^2 + 1 dr.

• Feb 14th 2013, 07:21 AM
Frankkair
Integral of r^2 times square root of 4r^2 + 1 dr.
Can anyone help me with this?

Attachment 27017

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• Feb 14th 2013, 07:42 AM
Plato
Re: Integral of r^2 times square root of 4r^2 + 1 dr.
Quote:

Originally Posted by Frankkair
Can anyone help me with this?

Attachment 27017?

Let $\displaystyle u = 4r^2 + 1\;,\,du = 8rdr.\;\& \,\begin{array}{*{20}c} r &\vline & 0 & 2 \\\hline u &\vline & 1 & {17} \\ \end{array}$

Thus $\displaystyle \int_1^{17} {\left( {\frac{{u - 1}}{4}} \right)\sqrt u \left( {\frac{{du}}{8}} \right)}$.
• Feb 14th 2013, 08:01 AM
Frankkair
Re: Integral of r^2 times square root of 4r^2 + 1 dr.
Thank you, but again I have a question (now a more basic one)

I got this, but I can't solve (guess my algebra is not working today)

Attachment 27019

Could u help me? Thanks!
• Feb 14th 2013, 10:51 AM
HallsofIvy
Re: Integral of r^2 times square root of 4r^2 + 1 dr.
Seriously? Just put "17" and "1" in for u and subtract. You really can't do much with $\displaystyle 17^{5/2}$ or $\displaystyle 17^{3/2}$ but, of course, $\displaystyle 1^{5/2}= 1^{3/2}= 1$.