# Foo - Express integral as limit of sums

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View Full Version : Express integral as limit of sums

phantomcow2
05-28-09, 09:33 PM
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?

x136
05-28-09, 09:41 PM
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Siu Blue Wind
05-28-09, 09:43 PM
*peeks in*

*leaves*

Tom Stormcrowe
05-28-09, 09:49 PM
lim_(n->+-infinity) cosh(2/n) = 1

Tom Stormcrowe
05-28-09, 09:50 PM
integral_1^3(2 x+cos(x)) dx = 8-sin(1)+sin(3)~~7.29965...

cal_gundert05
05-29-09, 02:05 PM
integral_1^3(2 x+cos(x)) dx = 8-sin(1)+sin(3)~~7.29965...

Did you check WolframAlpha (http://www40.wolframalpha.com/input/?i=integrate+2x+%2B+cos+x+dx+from+x%3D1+to+3), too?

Tom Stormcrowe
05-29-09, 02:48 PM
Did you check WolframAlpha (http://www40.wolframalpha.com/input/?i=integrate+2x+%2B+cos+x+dx+from+x%3D1+to+3), too?

No, I worked it out first, and then confirmed it afterward with Wolfram.