Riemann Sums Check

Front

What is a Riemann Sum?

Back

A Riemann Sum is a method for approximating the total area under a curve by dividing it into rectangles and summing their areas.

Front

What happens to the accuracy of a Riemann Sum as the number of rectangles increases?

Back

The more rectangles used, the better the approximation of the area under the curve.

Front

For a strictly increasing function, what type of estimate does a right-hand Riemann Sum provide?

Back

Overestimate.

Front

What does a Left Riemann Sum use to approximate the area under a curve?

Back

It uses the left endpoints of sub-intervals to form rectangles.

Front

What is the formula for a Left Riemann Sum with n sub-intervals?

Back

L_n = Σ f(x_i) * Δx, where x_i are the left endpoints.

Front

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

Back

A Left Riemann Sum uses left endpoints, while a Right Riemann Sum uses right endpoints of the sub-intervals.

Front

What is a Trapezoidal Sum?

Back

A Trapezoidal Sum approximates the area under a curve by dividing it into trapezoids instead of rectangles.

Front

How do you calculate a Trapezoidal Sum?

Back

T_n = (Δx/2) * (f(x_0) + 2Σf(x_i) + f(x_n)) for n intervals.

Front

What is the purpose of using Riemann Sums in calculus?

Back

Riemann Sums are used to approximate definite integrals.

Front

What is the relationship between Riemann Sums and definite integrals?

Back

As the number of rectangles increases, the Riemann Sum approaches the value of the definite integral.