4.1 Riemann Sum Practice

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.

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.

Front

For a strictly decreasing function, what type of estimate does a Right Riemann Sum provide?

Back

Underestimate.

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.

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.

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.

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)).

Front

What does a Right Riemann Sum represent visually?

Back

It represents the area under the curve using rectangles whose heights are determined by the right endpoints of the sub-intervals.

Front

What is the effect of increasing the number of sub-intervals on the accuracy of a Riemann Sum?

Back

Increasing the number of sub-intervals generally increases the accuracy of the Riemann Sum approximation.

Front

What is the Trapezoidal Sum?

Back

The Trapezoidal Sum is a method of approximating the area under a curve by dividing it into trapezoids instead of rectangles.