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Math Help - Finding the area between curve, tangent and y axis.

  1. #1
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    Finding the area between curve, tangent and y axis.

    Having difficulties solving the following question part c.

    Q15
    a)sketch the curve of e^x+2
    b)Find the equation of the tangent at x=-2. I worked this out to be y=x+3
    c)find the area between the curve, tangent and y axis.

    -i Know that the tangent equation x+3 and e^x+2 intersect at x=-2 and that the area bounded by the y axis should be between the two functions y intercepts which are 3 and e^2.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Finding the area between curve, tangent and y axis.

    I guess the function is: y=e^{x+2}
    b) right!
    c) Have you learned to integrate? ...
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  3. #3
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    Re: Finding the area between curve, tangent and y axis.

    Yes i sure have learned to integrate. For 'in between the curves' would i find the integral from 0 to -2 of e^x+2 - x+3? +(y axis) integral from e^2 to 3 of e^x+2 - x+3........
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Finding the area between curve, tangent and y axis.

    (Useful is to graph the functions, have you done that?)
    You've to calculate:
    \int_{-2}^{0} [e^{x+2}-(x+3)]dx
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