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Riemann Sum with subintervals/partitionby MelissaJL
Tags: riemann sum 
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#1
Jan1713, 10:31 PM

P: 36

So I missed a class and am trying to figure out a question in my textbook but am completely lost. It goes a little something like this:
Let f(x)=x^{3} and let P=<2,0,1,3,4> be a partition of [2,4]. a) Compute Riemann Sum S(f,P*) if the points <x_{1}*,x_{2}*,x_{3}*,x_{4}*>=<1,1,2,4> are embedded in P. Now I know how to calculate other Riemann Sums but I have not encountered one with a partition and subintervals yet. I tried to do the autodidactic thing and look up examples and videos but I could not find one similar to this. If I could get some help on how I approach this type of question that would be great. The answer is 79. Thanks :) 


#2
Jan1713, 11:21 PM

P: 1,460

What do you get when you compute this : [itex]\sum_{i=1}^{n} f(x_i)Δx_i[/itex] Where x_{i} is an arbitrary point in the i'th subinterval. 


#3
Jan1713, 11:33 PM

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PF Gold
P: 7,785

Δx_{1} = 2 = Δx_{3} . Δx_{2} = 1 = Δx_{4} . 


#4
Jan1813, 08:51 AM

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PF Gold
P: 39,300

Riemann Sum with subintervals/partition
The length of [2, 0] is 0(2)= 2, the length of [0, 1] is 1 0= 1, the length of [1, 3] is 3 1= 2, and the length of [3, 4] is 4 3= 1. So the Riemann sum is f(1)(2)+ f(1)(1)+ f(2)(2)+ f(4)(1) = 1^{3}(2)+ 1^{3}(1)+ 2^{3}(2)+ 4^{3}(1) 


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