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Please check if i am right - definite inegral

  1. Nov 29, 2009 #1
    The question:
    Use the definiton of the definite inegral (with right hand rule) to evaluate the following integral. Show work please
    Can NOT use shortcut method.. must be the long process

    Function:
    1
    S (3x^2 - 5x - 6) dx
    -4

    Work:
    ∫[-4,1] (3x^2 - 5x - 6) dx =
    lim[n-->∞] 5/n ∑[i=1 to n] {3(-4 + 5/n)² - 5(-4 + 5/n) - 6} =
    lim[n-->∞] 5*∑[i=1 to n] (48/n - 120i/n² + 75i²/n³ + 20/n -25i/n² - 6/n) =
    lim[n-->∞] 5*∑[i=1 to n] (62/n - 145i/n² + 75i²/n³) =
    lim[n-->∞] 5[62n/n - 145n(n+1)/(2n²) + 75n(n+1)(2n+1)/(6n³)] =
    5(62 - 145/2 + 25) = 72.5

    ∑[i=1 to n] 1 = n
    ∑[i=1 to n] i = n(n+1)/2
    ∑[i=1 to n] i² = n(n+1)(2n+1)/6


    Please check if this is correct and let me know
     
  2. jcsd
  3. Nov 29, 2009 #2

    Dick

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    That looks ok to me. Even if you can't use the 'shortcut method' to solve the problem, you can always use the shortcut method to check your work.
     
  4. Nov 29, 2009 #3
    it looks ok to me to =P, but i wanted to make sure if it's completely right

    -thanks =)
    which shortcut formula would i have to use
     
  5. Nov 29, 2009 #4

    Dick

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    I was assuming the 'shortcut' method was finding the antiderivative and evaluating it between the two limits. If you haven't learned that yet, then never mind.
     
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