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Math Help - Perimeter of a Region

  1. #1
    Newbie ZosoPage's Avatar
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    Perimeter of a Region

    How do I find the perimeter of the region bounded by y=e^x, y=0, x=0, and x=1?

    Mainly I need to know how to find the length of e^x from 0 to 1. I know that once I get this number I can just add the other sides (1, 1, and e^1).
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  2. #2
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    Quote Originally Posted by ZosoPage View Post
    How do I find the perimeter of the region bounded by y=e^x, y=0, x=0, and x=1?

    Mainly I need to know how to find the length of e^x from 0 to 1. I know that once I get this number I can just add the other sides (1, 1, and e^1).
    arc length of a function f(x) ...

    S = \int_a^b \sqrt{1 + \left[f'(x)\right]^2} \, dx
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  3. #3
    Newbie ZosoPage's Avatar
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    so

    \int_{0}^{1}\sqrt{1+e^{2x}}dx

    where do I go from here?
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  4. #4
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    Quote Originally Posted by ZosoPage View Post
    so

    \int_{0}^{1}\sqrt{1+e^{2x}}dx

    where do I go from here?
    your lack of knowledge in solving this and other basic calculus problems at this level is fairly evident.

    are you presently enrolled in a calculus class?
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  5. #5
    Newbie ZosoPage's Avatar
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    Yes I am, but I'm having a lot of trouble recently. I understood it all first semester but now the teacher does not explain things to us and she will not respond to e-mails when I ask her questions. Whenever I ask her things in class, she always has "somewhere she has to be" and says to email her my questions. That is why I came here to get help.
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  6. #6
    MHF Contributor
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    Quote Originally Posted by ZosoPage View Post
    so

    \int_{0}^{1}\sqrt{1+e^{2x}}dx

    where do I go from here?
    option 1 ... use technology to evaluate the integral.

    option 2 ... substitution, u^2 = 1 + e^{2x} . the process will involve partial fractions and the exact solution is rather ugly.

    option 3 ... trig substitution, e^x = \tan{\theta} . process will involve integration by parts.

    there may be other methods.
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