I started calc 2 this week. We're reviewing Reimann sums. I need to express the following as a limit of sums, but not calculate the limit.
Integral of (2x+cosx)dx from 1 to 3
So here I would find delta x, which is equal to -2/n. xi is equal to -2i/n
summation f(xi)(delta x)
summation (2(-2i/n) + cos(-2i/n))(-2/n)
summation (-8i/n^2) + (-2/n)cos(-2i/n)
summation (-8i/n^2) + summation [(2/n)cos(-2i/n)]
Okay now what? usually I'd factor out the -8/n^2 from the first term, and the (-2/n) from the second term, putting it in front of the summation (sigma). Then I'd use one of my formulas to substitute, such as n(n-1)/2. But I what formula exists for cos(-2i/n)? I can't factor anything out here. Am I already done?