# Thread: Finding area with integration

1. ## 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!

2. ## Re: Finding area with integration

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

3. ## Re: Finding area with integration

$\displaystyle \text{Area}= \int_1^5 \frac{x+6}{x}dx = \int_1^5 dx + 6\int_1^5 \frac{1}{x}dx$

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