Riemann Sum: Solve for Area Under Curve 0 to 18

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SUMMARY

The discussion focuses on calculating the area under the curve for the function f(x) = ∛x + 12 using Riemann sums from x = 0 to x = 18 with n = 6 subintervals. The user attempted to apply the formula Σ f(ci) Δxi, where ci = i³/n³, but encountered a discrepancy of 200 from the actual area. The user questions the correctness of their Riemann sum setup and whether limits are involved in the calculation.

PREREQUISITES
  • Understanding of Riemann sums and their applications in calculus.
  • Familiarity with the function f(x) = ∛x + 12.
  • Knowledge of partitioning intervals and calculating Δxi.
  • Basic grasp of limits in the context of definite integrals.
NEXT STEPS
  • Review the concept of Riemann sums and their formulas in calculus.
  • Practice calculating Δxi for different values of n in Riemann sums.
  • Explore the relationship between Riemann sums and definite integrals.
  • Investigate common errors in Riemann sum calculations and how to avoid them.
USEFUL FOR

Students studying calculus, particularly those learning about Riemann sums and area under curves, as well as educators looking for examples of common pitfalls in these calculations.

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Riemann sum help!

Homework Statement


Use Riemann sum with ci= i3/n3
f(x)= \sqrt[3]{x} +12
from x=0 to x=18
n= 6 subintervals
Approximate the sum using Riemann's Sum

Homework Equations


\Sigma f(ci) \Delta xi
is the equation for riemanns sum i think

The Attempt at a Solution


i tried plugging in stuff using that, but i must've done something wrong because the answer i got was 200 off the actual area under the curve...
 
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also, is my original equation for riemann's sum correct? is there a limit involved?
 

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