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Math Help - Evaluate the integral

  1. #1
    Member mybrohshi5's Avatar
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    Evaluate the integral

    Evaluate:


     \int ^1_0 \frac {d}{dx} (e^{arctan(x)})  dx


    This problem does not make sense to me?

    I am reading it as find the derivative  (\frac {d}{dx}) of the antiderivative? .... which does not make sense to me at all.

    I guess im just unsure how to do this problem in general.

    Any help would be great.

    Thank you.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by mybrohshi5 View Post
    Evaluate:


     \int ^1_0 \frac {d}{dx} (e^{arctan(x)}) dx


    This problem does not make sense to me?

    I am reading it as find the derivative  (\frac {d}{dx}) of the antiderivative? .... which does not make sense to me at all.

    I guess im just unsure how to do this problem in general.

    Any help would be great.

    Thank you.
    Surely the antiderivative of a derivative is the original function...

    So \int_0^1{\frac{d}{dx}\left(e^{\arctan{x}}\right)\,  dx} = \left[e^{\arctan{x}}\right]_0^1.
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by mybrohshi5 View Post
    Evaluate:


     \int ^1_0 \frac {d}{dx} (e^{arctan(x)}) dx


    This problem does not make sense to me?

    I am reading it as find the derivative  (\frac {d}{dx}) of the antiderivative? .... which does not make sense to me at all.

    I guess im just unsure how to do this problem in general.

    Any help would be great.

    Thank you.
    The integral

    \int_a^b\frac{d}{dx}f(x)dx=f(b)-f(a)...

    Think about it. You take the derivative of a function, then integrate the function, leaving you with the original function. I think the point to the excersie is to show that differentiation and integration are inverse processes.
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  4. #4
    Member mybrohshi5's Avatar
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    Thank you. that does make sense i was not thinking straight at that moment haha.


    how would i go about doing

     \frac {d}{dx} \int ^1_0 e^{arctan(x)} dx


    Thank you. This is helping me understand a lot for my final exam coming up =)
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  5. #5
    Member mybrohshi5's Avatar
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    Would i evaluate the integral first and then take the derivative of that number?

    if so the derivative of a number is just 0 so is that the answer to this second one?

    just zero?
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by mybrohshi5 View Post
    Would i evaluate the integral first and then take the derivative of that number?

    if so the derivative of a number is just 0 so is that the answer to this second one?

    just zero?
    Yes. In this case, we are dealing with a definite integral. This implies that you are taking the derivative of a constant.
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