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 05-28-09, 08:33 PM #1 phantomcow2 la vache fantôme Thread Starter     Join Date: Aug 2004 Location: NH Bikes: Posts: 6,266 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) 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? __________________ C://dos C://dos.run run.dos.run
 05-28-09, 08:41 PM #2 x136  phony collective progress     Join Date: Sep 2006 Location: San Hoosey Bikes: http://velospace.org/user/36663 Posts: 2,981 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Welcome ... to MathCom. This ... is ... MathCom. Welcome. This is MathCom. Welcome ... to MathCom. You can do anything at MathCom. Anything at all. The only limit is yourself. Welcome ... to MathCom. Welcome ... to MathCom. This is ... MathCom. Welcome ... to MathCom. This is MathCom. Welcome! Yes. This ... is MathCom. This is MathCom. And welcome to you, have come to MathCom. Anything ... is possible ... at MathCom. You can do ... anything at MathCom. The infinite is possible at MathCom. The unattainable is unknown at MathCom. Welcome to MathCom. This ... is MathCom. Welcome to MathCom. Welcome. This ... is ... MathCom. Welcome to MathCom! Welcome ... to MathCom. __________________ Last edited by x136; 05-28-09 at 09:11 PM.
05-28-09, 08:43 PM   #3
Siu Blue Wind
I don't think so

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 05-28-09, 08:49 PM #4 Tom Stormcrowe Out fishing with Annie on his lap, a cigar in one hand and a ginger ale in the other, watching the sunset.     Join Date: Mar 2006 Location: South Florida Bikes: Techna Wheelchair and a Sun EZ 3 Recumbent Trike Posts: 16,128 Mentioned: 1 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) lim_(n->+-infinity) cosh(2/n) = 1 __________________ . “He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.”- Fredrick Nietzsche "We can judge the heart of a man by his treatment of animals." - Immanuel Kant
 05-28-09, 08:50 PM #5 Tom Stormcrowe Out fishing with Annie on his lap, a cigar in one hand and a ginger ale in the other, watching the sunset.     Join Date: Mar 2006 Location: South Florida Bikes: Techna Wheelchair and a Sun EZ 3 Recumbent Trike Posts: 16,128 Mentioned: 1 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) integral_1^3(2 x+cos(x)) dx = 8-sin(1)+sin(3)~~7.29965... __________________ . “He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.”- Fredrick Nietzsche "We can judge the heart of a man by his treatment of animals." - Immanuel Kant
05-29-09, 01:05 PM   #6
cal_gundert05
My name is Mike, not Cal

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 Originally Posted by Tom Stormcrowe integral_1^3(2 x+cos(x)) dx = 8-sin(1)+sin(3)~~7.29965...
Did you check WolframAlpha, too?

05-29-09, 01:48 PM   #7
Tom Stormcrowe
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 Originally Posted by cal_gundert05 Did you check WolframAlpha, too?
No, I worked it out first, and then confirmed it afterward with Wolfram.
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