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Math Help - Integral : substitution & by parts of an exponential

  1. #1
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    Integral : substitution & by parts of an exponential

    Hello,
    Quote Originally Posted by Firstone
    Hi there, I was wondering if you could steer me ikn the right direction with an assignment question. It's a definite integral question.

    Integral e^(sqrt{x}) dx (from 1 to 4)

    It says i'm suppose to use substiution then integration by parts.

    but I can't really see why I use substitution, it didn't makew anything easier.

    I let u = sqrt{x}

    I ended up with Integral e^(sqrt{x}) * 2du/sqrt{x}

    I was just wondering if i did the substitution part right?
    No, but you didn't substitute at all

    \sqrt{x}=u \implies du=\frac{dx}{2 \sqrt{x}} \implies dx=2 \sqrt{x} ~du \neq \frac{2 du}{\sqrt{x}}

    Transform your integral : every x has to disappear. So as soon as you encounter \sqrt{x}, change it into u. If there was x that you encounter, then x=u^2 and substitute too.

    And then integrate by parts as recommended. Don't forget to either change the boundaries of the integral, either to substitute back u.



    P.S. : please next time, post a new thread. It may be useful for some other people (and my PM box is overwhelmed by all these messages lol!)
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  2. #2
    Newbie Firstone's Avatar
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    Yeah i noticed i did the dx part wrong, was about to send another pm hehe.
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  3. #3
    Newbie Firstone's Avatar
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    Yay i got the right answer, i forgot that i had to get rid of each x with the substiution rule.

    Thanks again for ur help. =)
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