# Finding area with integration

• Jun 28th 2012, 10:03 PM
TWN
Finding area with integration
Find the area of the region bounded by the graphs of the following equations:

y = (x + 6) / x
x = 1
x = 5
y = 0

Please show me how to do the above problem using integration. The natural log is supposed to be used in this somehow but I'm completely lost. Thank you in advance!
• Jun 28th 2012, 10:38 PM
biffboy
Re: Finding area with integration
Quote:

Originally Posted by TWN
Find the area of the region bounded by the graphs of the following equations:

y = (x + 6) / x
x = 1
x = 5
y = 0

Please show me how to do the above problem using integration. The natural log is supposed to be used in this somehow but I'm completely lost. Thank you in advance!

y=(x+6)/x=1+6/x Integrating get x+6logx Between the limits 1 and 5 we get for the area (5+6log5)-(1+6log1)=4+6log5
• Jun 29th 2012, 05:28 AM
sbhatnagar
Re: Finding area with integration
$\displaystyle \text{Area}= \int_1^5 \frac{x+6}{x}dx = \int_1^5 dx + 6\int_1^5 \frac{1}{x}dx$

$\displaystyle =(5-1)+6(\ln 5 - \ln 1)=4+6 \ln 5$