Reimann & Trapezoidal Sums

Flashcard
•
Mathematics
•
12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a Left Riemann Sum?
Back
A method for approximating the area under a curve by using the left endpoints of subintervals to determine the height of rectangles.
2.
FLASHCARD QUESTION
Front
How do you calculate a Left Riemann Sum with 4 sub-intervals?
Back
Multiply the function values at the left endpoints of each sub-interval by the width of the sub-intervals and sum the results.
3.
FLASHCARD QUESTION
Front
What is a Trapezoidal Sum?
Back
A method for estimating the area under a curve by averaging the heights of the function at the endpoints of subintervals and multiplying by the width of the subintervals.
4.
FLASHCARD QUESTION
Front
How do you calculate a Trapezoidal Sum?
Back
Use the formula: T = (b-a)/n * (f(a) + 2 * Σf(x_i) + f(b)), where n is the number of subintervals.
5.
FLASHCARD QUESTION
Front
What is the significance of using 3 equal subintervals in a Trapezoidal Sum?
Back
It allows for a more accurate approximation of the area under the curve by evenly distributing the intervals.
6.
FLASHCARD QUESTION
Front
What happens to the estimate when using a Right Riemann Sum for a strictly decreasing function?
Back
It results in an underestimate of the actual area under the curve.
7.
FLASHCARD QUESTION
Front
What is the formula for calculating the area using a Right Riemann Sum?
Back
Multiply the function values at the right endpoints of each sub-interval by the width of the sub-intervals and sum the results.
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