Can anyone help with finding the Riemann sum for f(x)=x^3?

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SUMMARY

The discussion focuses on calculating the Riemann sum for the function f(x)=x^3 over the interval [1,5] using an equipartition P=(1,2,3,4,5) divided into 4 intervals. The right-hand endpoints are utilized for the calculation, specifically using the formula for the summation of cubes, sum(i^3)=1/4n^2(n+1)^2. Participants emphasize the importance of showing initial work to receive effective assistance in homework-related queries.

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  • Familiarity with the function f(x)=x^3
  • Knowledge of summation formulas, particularly for cubes
  • Basic skills in interval partitioning and endpoint selection
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dan
Hello there, can anyone help me here as I'm finding it difficult to tackle this question.

Consider f(x)=x^3 on the interval [1,5].
Find the Riemann sum for the equipartition P=(1,2,3,4,5) into 4 intervals with x_i^* being the right-hand endpoints (ie. x_i=a+hi)

Then find a formula for the Riemann sum for an equipartition P_n into n intervals and right-hand endpoints. Use the summation formulae
sum(i^3)=1/4n^2(n+1)^2, upper lim=n, lower lim;i=1.

Cheers
 
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Hi dan,
I believe this belongs in Homework Help and the policy there is that you tell us what you got so far, and where you are stuck. Then we can help.
 

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