Which Riemann Sums is best?
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Different methods provide differing levels of accuracy dependent on the function itself.
Scenario: Given the function and its corresponding graph below, determine which Riemann sum is most accurate for calculating the area under the curve from x = 0 to x = 20 with 4 rectangles.
Area = 143.75
Area = 193.75
Area = 165.625
| Method | Solution |
|---|---|
| Left Riemann Sums | 143.75 |
| Right Riemann Sums | 193.75 |
| Midpoint Riemann Sums | 165.625 |
| Exact Answer | 166.667 |
PRO TIP: The Midpoint method does a good job of canceling out underestimates and overestimates.
Remember, different methods result in different levels of accuracy!
Don't always assume the Left Riemann will underestimate, Right Riemann will overestimated, etc.