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Math Help - Finding area with integration

  1. #1
    TWN
    TWN is offline
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    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!
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  2. #2
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    Re: Finding area with integration

    Quote Originally Posted by TWN View Post
    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
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  3. #3
    Member sbhatnagar's Avatar
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    Re: Finding area with integration

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

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