What is the Riemann Sum Approximation for this Homework Problem?

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SUMMARY

The discussion focuses on the Riemann Sum approximation method for calculating the area under a curve using rectangles. The user applies a left-handed approximation with x-values of 0, 0.5, 1, and 1.5, resulting in corresponding y-values of 6, 3, 2, and 1.5. The final calculation yields an area of 25/4, confirming the accuracy of the approximation. This method utilizes the formula for the area of rectangles, which is the product of the change in x and the function value f(x).

PREREQUISITES
  • Understanding of Riemann Sums
  • Knowledge of calculus concepts, specifically integration
  • Familiarity with left-handed approximation techniques
  • Basic algebra for arithmetic calculations
NEXT STEPS
  • Study the differences between left-handed and right-handed Riemann sums
  • Explore the concept of definite integrals in calculus
  • Learn about the trapezoidal rule for area approximation
  • Practice with more complex functions and their Riemann sum approximations
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Students in calculus courses, educators teaching integration techniques, and anyone looking to enhance their understanding of numerical methods for area approximation.

Qube
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Homework Statement



https://scontent-b-mia.xx.fbcdn.net/hphotos-prn2/v/1456973_10201043975243279_1765184125_n.jpg?oh=05b39611ad70d28d837ed219e1b0f2aa&oe=52838593

Homework Equations



The area can be approximated by using the sum of the areas of the rectangles. Area of rectangle = change in x * y (given by f(x)).

The Attempt at a Solution



I've taken calculus I, II, and diff eqs., but I haven't done this for a while. I'm doing it mostly from intuition and memory.

My x-values are 0, 0.5, 1, and 1.5. This gives me the x-values for a left-handed approximation since I'm not going up to 2.

My y-values are therefore 6, 3, 2, and 3/2.

0.5(6) + 0.5(3) + 0.5(2) + 0.5(3/2) = 3 + 3/2 + 1 + 3/4 = 25/4.
 
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Qube said:

Homework Statement



https://scontent-b-mia.xx.fbcdn.net/hphotos-prn2/v/1456973_10201043975243279_1765184125_n.jpg?oh=05b39611ad70d28d837ed219e1b0f2aa&oe=52838593

Homework Equations



The area can be approximated by using the sum of the areas of the rectangles. Area of rectangle = change in x * y (given by f(x)).

The Attempt at a Solution



I've taken calculus I, II, and diff eqs., but I haven't done this for a while. I'm doing it mostly from intuition and memory.

My x-values are 0, 0.5, 1, and 1.5. This gives me the x-values for a left-handed approximation since I'm not going up to 2.

My y-values are therefore 6, 3, 2, and 3/2.

0.5(6) + 0.5(3) + 0.5(2) + 0.5(3/2) = 3 + 3/2 + 1 + 3/4 = 25/4.
That is correct.
 
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