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Math Help - area under exponential function

  1. #1
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    area under exponential function

    Using simultaneous equations I have worked out my exponential function for the top left hand corner of the attached picture to be:

    f(x) = 10.767 (1.346)^x

    I need to find the area under this graph in the top left hand corner of the attached picture. I am need of some assistance please.
    Attached Thumbnails Attached Thumbnails area under exponential function-picture.jpg  
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Mr.Ree View Post
    Using simultaneous equations I have worked out my exponential function for the top left hand corner of the attached picture to be:

    f(x) = 10.767 (1.346)^x

    I need to find the area under this graph in the top left hand corner of the attached picture. I am need of some assistance please.
    Area under f(x) to the left of x=u is:

    \int_0^u f(x) \;dx= 10.767 \int_0^u e^{x\ln(1.346)}\;dx

    ................ =\frac{10.767}{\ln(1.346)} \left[e^{x\ln(1.346)}\right]^u_0

    ................ =\frac{10.767}{\ln(1.346)} (1.346^u-1)

    or if you want the actual area shown in the figure (including the initial rectangular bit) you want:

    A=8+\int_1^8 f(x) \;dx=8+\frac{10.767}{\ln(1.346)} (1.346^8-1.346)

    CB
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