# Work done integration of cylinder volume

• Jun 13th 2012, 07:32 AM
Jelley
Work done integration of cylinder volume
Hi Guys , im new here , i could do with a hand with this integration question , cant get my head round where to start , any help would be greatly appreciated
The attached is the copy of the question ,
Thanks
Simon
• Jun 13th 2012, 07:40 AM
Reckoner
Re: Work done integration of cylinder volume
Quote:

Originally Posted by Jelley
Hi Guys , im new here , i could do with a hand with this integration question , cant get my head round where to start , any help would be greatly appreciated
The attached is the copy of the question

So

$\displaystyle W = \int_{30}^{80}\frac{175}V\,dV$

If you can't integrate that, then you need some review. What is $\displaystyle \int\frac{dx}x?$
• Jun 13th 2012, 07:44 AM
skeeter
Re: Work done integration of cylinder volume
http://mathhelpforum.com/attachments...3-16.20.35.png

$\displaystyle W = \int_{30}^{80} \frac{175}{V} \, dV$

basic log antiderivative ...

$\displaystyle W = 175 \left[\ln{V}\right]_{30}^{80} = 175\left[\ln(80) - \ln(30)\right] = 175\ln\left(\frac{8}{3}\right) \approx 172\, J$