Riemann sums

Front

What is a Riemann Sum?

Back

A Riemann Sum is a method for approximating the area under a curve using rectangles. The more rectangles used, the better the approximation.

Front

What is another term for 'integral'?

Back

Antiderivative

Front

What does a right-hand Riemann Sum do for a strictly increasing function?

Back

It provides an overestimate of the area under the curve.

Front

How does the number of rectangles affect the approximation in a Riemann Sum?

Back

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

Front

What is the approximate area under the curve using 4 intervals with left values if the heights are 2, 2, 3, and 3?

Back

10

Front

What is the formula for a definite integral?

Back

The definite integral from a to b of f(x) dx represents the area under the curve f(x) from x=a to x=b.

Front

What is the difference between a left-hand and right-hand Riemann Sum?

Back

A left-hand Riemann Sum uses the left endpoints of intervals to determine the height of rectangles, while a right-hand Riemann Sum uses the right endpoints.

Front

What is the significance of the limit of Riemann Sums as the number of rectangles approaches infinity?

Back

It defines the exact value of the definite integral.

Front

In the context of Riemann Sums, what does 'partition' refer to?

Back

A partition is a division of the interval [a, b] into smaller subintervals.

Front

What is the relationship between Riemann Sums and the Fundamental Theorem of Calculus?

Back

The Fundamental Theorem of Calculus connects differentiation and integration, showing that the integral of a function can be evaluated using its antiderivative.