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Old 05-28-09, 08:33 PM   #1
phantomcow2
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Express integral as limit of sums

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?
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Old 05-28-09, 08:41 PM   #2
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Old 05-28-09, 08:43 PM   #3
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Old 05-28-09, 08:49 PM   #4
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lim_(n->+-infinity) cosh(2/n) = 1
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Old 05-28-09, 08:50 PM   #5
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integral_1^3(2 x+cos(x)) dx = 8-sin(1)+sin(3)~~7.29965...
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Old 05-29-09, 01:05 PM   #6
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Originally Posted by Tom Stormcrowe View Post
integral_1^3(2 x+cos(x)) dx = 8-sin(1)+sin(3)~~7.29965...
Did you check WolframAlpha, too?
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Old 05-29-09, 01:48 PM   #7
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Did you check WolframAlpha, too?
No, I worked it out first, and then confirmed it afterward with Wolfram.
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