Riemann Sum Practice

Riemann Sum Practice

Assessment

Flashcard

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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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 region into smaller sub-intervals and summing the areas of rectangles formed by the function values at specific points.

2.

FLASHCARD QUESTION

Front

What is the difference between Left Riemann Sum and Right Riemann Sum?

Back

In a Left Riemann Sum, the height of each rectangle is determined by the function value at the left endpoint of each sub-interval, while in a Right Riemann Sum, the height is determined by the function value at the right endpoint.

3.

FLASHCARD QUESTION

Front

What is the Trapezoidal Rule?

Back

The Trapezoidal Rule is a numerical method for estimating the integral of a function by approximating the area under the curve as a series of trapezoids rather than rectangles.

4.

FLASHCARD QUESTION

Front

How do you calculate the area using Left Riemann Sum?

Back

To calculate the area using Left Riemann Sum, multiply the width of each sub-interval by the function value at the left endpoint and sum these products.

5.

FLASHCARD QUESTION

Front

What is the formula for the Trapezoidal Rule?

Back

The formula for the Trapezoidal Rule is: T = (b-a)/(2n) * (f(a) + 2 * Σf(x_i) + f(b)), where n is the number of sub-intervals.

6.

FLASHCARD QUESTION

Front

What does 'n' represent in Riemann Sums?

Back

In Riemann Sums, 'n' represents the number of sub-intervals into which the total interval is divided.

7.

FLASHCARD QUESTION

Front

How do you determine the width of each sub-interval in Riemann Sums?

Back

The width of each sub-interval is determined by the formula: Δx = (b - a) / n, where [a, b] is the interval and n is the number of sub-intervals.

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