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Math Help - Expressing a limit as definite Integral

  1. #1
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    Expressing a limit as definite Integral

    Hi, I am stuck on this question that asks me to express the following limit to infinity as a definite integral.
    Expressing a limit as definite Integral-capture.png
    I am sort of stuck. If let delta x=3/n and the second part equal xi, I get that it is the integral of x^9 from 0 to 8.

    However shouldn't it be something else?


    Thanks in advance!

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    Quote Originally Posted by KelvinScc View Post
    Hi, I am stuck on this question that asks me to express the following limit to infinity as a definite integral.
    Click image for larger version. 

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    I am sort of stuck. If let delta x=3/n and the second part equal xi, I get that it is the integral of x^9 from 0 to 8.

    However shouldn't it be something else?


    Thanks in advance!

    You are correct you get

    \displaystyle \Delta x = \frac{3}{n}

    then

    \displaystyle x_i=a+i\Delta x = a+\frac{3i}{n}

    When i=0 you get a and when i=n you get b

    So from you formula a=... and b=...

    and you f is correct f(x)=x^9
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