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autodidude
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Homework Statement
Original problem asked me to prove [tex]\int_a^b \! x \, \mathrm{d} x = \frac{b^2-a^2}{2}[/tex] using Riemann sums. I've already seen a simpler formula using the left side of the rectangles but I'm curious as to how you would manipulate the formula below by hand to get the answer
Homework Equations
[tex]\lim_{n\rightarrow \infty}\sum_{i=1}^{n}[\frac{(b-a)i}{n}+a][\frac{b-a}{n}][/tex]
The Attempt at a Solution
pages and pages of algebra leading nowhere!