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

Find the area bounded between the two curves

y=34ln(x) and y=xln(x)

2. Relevant equations

Integration by parts: [tex]\int[/tex]udv= uv-[tex]\int[/tex]vdu

3. The attempt at a solution

First I found the intersection points of the two equation to set the upper and lower bounds. The lower bound is 0 and the upper bound is 34. My integrand is as follows--

[tex]\int[/tex]34ln(x)-xln(x) with the limits of integration being from 0 to 34.

I evaluated the integral using integration by parts, and eventually came up with the following solution...

[tex]\int[/tex]34ln(x)-xln(x)= 34xln(x)-34x-(x[tex]^{2}[/tex]ln(x)/2) -(1/4)x[tex]^{2}[/tex]

and evaluated from 0 to 34, the answer is 1156ln(34)-1156-(1156ln(34)/2)+289

I am not quite sure where my mistake is being made. I verified my answer using a graphing calculator (although that does not absolutely make my answer correct), so if anyone sees where I am making my mistake I would greatly appreciate the help!

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# Homework Help: Area of the region bounded between two curves with integration by parts

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