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macilath
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Homework Statement
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]
Homework 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
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.
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