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Math Help - Q2iiA8-integration

  1. #1
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    Q2iiA8-integration

    Hi:
    I have this differentiation problem which am completely not sure about. I have done the question part way, but would like to know if am heading in the right direction before I take the next step.
    Could you please take a look and advise
    thank you

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  2. #2
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    That looks difficult - better substitute u = 7 + e^(2x)
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  3. #3
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    You mean?

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  4. #4
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    Just in case a picture helps...



    ... where



    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    The general drift being...



    Spoiler:

    _________________________________________
    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
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  5. #5
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    So this leaves me with a quotient. Should i now use integration by parts?

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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by stealthmaths View Post
    Hi:
    I have this differentiation problem which am completely not sure about. I have done the question part way, but would like to know if am heading in the right direction before I take the next step.
    Could you please take a look and advise
    thank you

    You could just observe that:

    \frac{d}{dx} \left[\frac{1}{3}(7+e^{2x})^{3/2}\right]=e^{2x}(7+e^{2x})^{1/2}

    then use the fundamental theorem of calculus to find the integral.

    CB
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  7. #7
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    hi:
    so I have got 143.0 (3s.f.)
    is this correct please?
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by stealthmaths View Post
    hi:
    so I have got 143.0 (3s.f.)
    is this correct please?
    Other than that being four significant figures yes.

    CB
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  9. #9
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    thanks Captain Black
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