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Math Help - area between a line and a curve

  1. #1
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    area between a line and a curve

    How do i find the area of of the region bounded by the curve y=e^2x, the x-axis, and x=2

    i know you need to integrate it but i'm not sure how to set it up.
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  2. #2
    MHF Contributor

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    I presume that you know that the "area under a curve", the area between the graph and the x-axis, between, say, x= a and x= b, is the integral of the function from a to b. In this case, there is only one x bound given but y= e^{2x} goes to 0 as x goes to negative infinity so that the three lines, y= e^{2x}, y= 0, and x= 2 do bound a "region". The area is \int_{-\infty}^2 e^{2x} dx. Integrate \int_a^2 e^{2x} dx and then take the limit as a goes to negative infinity.
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