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!

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

Re: Finding area with integration

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

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