Riemann Sums

Front

What is a Riemann Sum?

Back

A method for approximating the total area under a curve by dividing it into smaller intervals and summing the areas of rectangles or trapezoids.

Front

What are the types of Riemann Sums?

Back

Left Riemann Sum, Right Riemann Sum, and Middle Riemann Sum.

Front

How do you calculate a Left Riemann Sum?

Back

By using the left endpoints of each interval to determine the height of the rectangles.

Front

How do you calculate a Right Riemann Sum?

Back

By using the right endpoints of each interval to determine the height of the rectangles.

Front

What is a Middle Riemann Sum?

Back

A Riemann Sum that uses the midpoints of each interval to determine the height of the rectangles.

Front

What is the formula for calculating the area using Riemann Sums?

Back

Area ≈ Σ (height of rectangles × width of intervals).

Front

What is the significance of increasing the number of intervals in Riemann Sums?

Back

Increasing the number of intervals generally leads to a more accurate approximation of the area under the curve.

Front

What is the Trapezoidal Rule?

Back

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

Front

What is the difference between Riemann Sums and the Trapezoidal Rule?

Back

Riemann Sums use rectangles to approximate area, while the Trapezoidal Rule uses trapezoids.

Front

What is the relationship between Riemann Sums and definite integrals?

Back

Riemann Sums are used to approximate definite integrals, which represent the exact area under a curve.