
4.1 Riemann Sum Practice
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a Riemann Sum?
Back
A Riemann Sum is a method for approximating the total area under a curve by dividing the area into rectangles and summing their areas.
2.
FLASHCARD QUESTION
Front
What is the difference between a Left Riemann Sum and a Right Riemann Sum?
Back
A Left Riemann Sum uses the left endpoints of sub-intervals to determine the height of rectangles, while a Right Riemann Sum uses the right endpoints.
3.
FLASHCARD QUESTION
Front
For a strictly decreasing function, what type of estimate does a Right Riemann Sum provide?
Back
Underestimate.
4.
FLASHCARD QUESTION
Front
What does a Left Riemann Sum represent visually?
Back
It represents the area under the curve using rectangles whose heights are determined by the left endpoints of the sub-intervals.
5.
FLASHCARD QUESTION
Front
How do you calculate the area using a Left Riemann Sum with 4 sub-intervals?
Back
Multiply the height of each rectangle (using left endpoints) by the width of the sub-intervals and sum them up.
6.
FLASHCARD QUESTION
Front
What is the formula for a Left Riemann Sum?
Back
L = Σ f(x_i) * Δx, where f(x_i) is the function value at the left endpoint and Δx is the width of the sub-interval.
7.
FLASHCARD QUESTION
Front
What is the approximate area under the curve using a Left Riemann Sum with heights 3, 4, 5, and 7?
Back
10 (calculated as 5(3) + 1(4) + 2(5) + 1(7)).
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