Reimann & Trapezoidal Sums

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.

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.

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.

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.

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.

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.

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.

Front

What is the difference between Left and Right Riemann Sums?

Back

Left Riemann Sums use the left endpoints for height, while Right Riemann Sums use the right endpoints.

Front

What is the effect of increasing the number of subintervals on the accuracy of Riemann Sums?

Back

Increasing the number of subintervals generally increases the accuracy of the approximation.

Front

What is an Overestimate in the context of Riemann Sums?

Back

An estimate that is greater than the actual area under the curve.