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Use the definition of the definite integral (with right hand rule) to evaluate

  1. Jul 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Use the definition of the definite integral (with right hand rule) to evaluate the following integral from -3 to 2
    [tex]\int(4x^2-9x+2)dx[/tex]

    2. Relevant equations
    [tex]\int[/tex] from a to b of f(x)dx = limit as [tex]n\rightarrow[/tex][tex]\infty[/tex] of [tex]\sum f(xi)\Deltax[/tex]. i = 1


    3. The attempt at a solution
    I found delta x = (b-a)/n, so delta x = 5/n.
    Then,
    limit as [tex]n\rightarrow[/tex][tex]\infty[/tex] of [tex]\sum (4(i/n)^2-9(i/n)+2)(5/n)[/tex].
    I distributed the (5/n) out, and a little algebra later, got that
    limit as [tex]n\rightarrow[/tex][tex]\infty[/tex] of [tex]\sum ((20i^2)/n^3)-(45i/n^2)+(10/n)[/tex].
    This is where I get stuck, I'm not sure how to simplify this to evaluate the limit.

    Thanks for any help!

    Edit: Sorry for sloppy forum code. LaTEX is new to me.
     
    Last edited: Jul 7, 2009
  2. jcsd
  3. Jul 7, 2009 #2

    jgens

    User Avatar
    Gold Member

    Assuming you've done all the math right up to this point, you just need some summation formulas to finish evaluating the integral.

    k = nk

    i = n(n+1)/2

    i2 = n(n+1)(2n+1)/6
     
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