Using Reimann sum to estimate the value of a double integral

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SUMMARY

The discussion focuses on estimating the value of the double integral ∫∫R(y² − 2x²) dA over the region R = [−3, 1] × [−2, 0] using a Riemann sum with m = 4 and n = 2. Participants clarify that the task is to utilize Riemann sums rather than calculating the indefinite integral, which was mistakenly attempted. The correct approach involves taking sample points from the upper left corners of the squares formed by the partitioning of the region.

PREREQUISITES
  • Understanding of Riemann sums
  • Familiarity with double integrals
  • Knowledge of partitioning regions in calculus
  • Basic algebraic manipulation of functions
NEXT STEPS
  • Study the application of Riemann sums in estimating double integrals
  • Learn how to partition regions for Riemann sums
  • Explore the differences between Riemann sums and indefinite integrals
  • Practice calculating double integrals using numerical methods
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Students and educators in calculus, mathematicians interested in numerical methods, and anyone looking to deepen their understanding of estimating integrals using Riemann sums.

carl123
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If R = [−3, 1] × [−2, 0], Use a Riemann sum with m = 4, n = 2 to estimate the value of ∫∫R(y2 − 2x2) dA. Take the sample points to be the upper left corners of the squares.

So far,

I found the indefinite integral of the function to be y3/3 - 2x3/3

Not sure where to go from here
 
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carl123 said:
If R = [−3, 1] × [−2, 0], Use a Riemann sum with m = 4, n = 2 to estimate the value of ∫∫R(y2 − 2x2) dA. Take the sample points to be the upper left corners of the squares.

So far,

I found the indefinite integral of the function to be y3/3 - 2x3/3

Not sure where to go from here

Why are you integrating at all? You were told to use Riemann Sums to ESTIMATE the integral!
 

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