# Math Help - Evaluating this Integral using the Definition

1. ## 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

2. Originally Posted by drain
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

3. 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!