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Math Help - Evaluating this Integral using the Definition

  1. #1
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    Evaluating this Integral using the Definition

    so i was to evaluate the integral of (x^2 + 5x + 3)dx with an upper limit of 5 and a lower limit of 1 using the definition of the integral (sorry I don't know how to do the notation on here)

    I got dx = 4/n

    lim n->infinity summed from i=1 to n [(1+ (4i/n))^2 + 5(1+(4i/n)) + 3)(4/n)

    this simplified to lim n->infinity summed from i=1 to n [(112i)/(n^2) + (64i^2)/(n^3) + 36/n)

    this is equal to lim n->infinity [(112/n^2)((n(n+1))/2) + ((64n)(n+1)(2n+1))/(6n^3) + (n)(6/n)]

    when I simplified and evaluated the limit I ended up with 250/3 ... am I close? Thanks for the help guys
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by drain View Post
    so i was to evaluate the integral of (x^2 + 5x + 3)dx with an upper limit of 5 and a lower limit of 1 using the definition of the integral (sorry I don't know how to do the notation on here)

    I got dx = 4/n

    lim n->infinity summed from i=1 to n [(1+ (4i/n))^2 + 5(1+(4i/n)) + 3)(4/n)

    this simplified to lim n->infinity summed from i=1 to n [(112i)/(n^2) + (64i^2)/(n^3) + 36/n)

    this is equal to lim n->infinity [(112/n^2)((n(n+1))/2) + ((64n)(n+1)(2n+1))/(6n^3) + (n)(6/n)]

    when I simplified and evaluated the limit I ended up with 250/3 ... am I close? Thanks for the help guys
    well, you could check your answer with regular integration to see if you are close.

    int{from 1 to 5}(x^2 + 5x + 3)dx = (1/3)x^3 + (5/2)x^2 + 3x evaluated between 1 and 5
    .............................................= (1/3)(5)^3 + (5/2)(5)^2 + 3(5) - (1/3) - (5/2) - 3
    .............................................= 125/3 + 125/2 + 15 - 1/3 - 5/2 - 3
    .............................................= 340/3

    hmmm, i'd expect the answer to be closer than that. recheck your work
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  3. #3
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    Gah I misplaced a 2. I got the same answer as you now. I didn't know how to re-check my work... we just started doing these things I still don't really know what I'm doing lol. But thanks man!
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