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Math Help - Calculate The Following Integral

  1. #1
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    Calculate The Following Integral

    Hello! The problem is:

    Calculate The Following Integral:

    (e^x + e^-x) from ln2 to ln3.

    I'm pretty sure the next step is to change it to (e^x - e^-x) as those are the anti-derivatives right? Or maybe I'm starting horrible hence why I can't solve it.

    Thanks in advance for any help! I've been stuck only on this one problem for hours!
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  2. #2
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    re: Calculate The Following Integral

    Quote Originally Posted by antz215 View Post
    Hello! The problem is:

    Calculate The Following Integral:

    (e^x + e^-x) from ln2 to ln3.

    I'm pretty sure the next step is to change it to (e^x - e^-x) as those are the anti-derivatives right?
    You can always find help here.

    Know that e^{\ln(3)}=3~\&~e^{-\ln(3)}=\frac{1}{3}~.
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  3. #3
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    re: Calculate The Following Integral

    Quote Originally Posted by antz215 View Post
    Hello! The problem is:

    Calculate The Following Integral:

    (e^x + e^-x) from ln2 to ln3.

    I'm pretty sure the next step is to change it to (e^x - e^-x) as those are the anti-derivatives right? Or maybe I'm starting horrible hence why I can't solve it.

    Thanks in advance for any help! I've been stuck only on this one problem for hours!
    It's easy to check isn't it: the derivative of e^x- e^{-x} is e^x-(-1)e^{-1}= e^x+ e^{-x} so yes, an anti-derivative of e^x+ e^{-x} is e^x- e^{-x}.

    Fundamental theorem of Calculus: if F(x) is an anti-derivative of f(x) then \int_a^b f(x)dx= F(b)- F(a).
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  4. #4
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    re: Calculate The Following Integral

    From both helps I am getting:

    e^x + e^-x dx
    (e^x - e^-x)
    (e^ln3 - e^-ln3) - (e^ln2 - e^-ln2)
    3 - 1/3 - 2 + 1/2
    = 7/6

    I think that is correct? Thanks for your guys' help!
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  5. #5
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    Re: Calculate The Following Integral

    Yes, that is correct. Congratulations!
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