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

1. Jul 7, 2009

### macilath

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
$$\int(4x^2-9x+2)dx$$

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

3. The attempt at a solution
I found delta x = (b-a)/n, so delta x = 5/n.
Then,
limit as $$n\rightarrow$$$$\infty$$ of $$\sum (4(i/n)^2-9(i/n)+2)(5/n)$$.
I distributed the (5/n) out, and a little algebra later, got that
limit as $$n\rightarrow$$$$\infty$$ of $$\sum ((20i^2)/n^3)-(45i/n^2)+(10/n)$$.
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. Jul 7, 2009

### jgens

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