What is the relationship between Riemann sums and monotonic functions?

The left Riemann sum amounts to an overestimation if f is monotonically decreasing on this interval, and an underestimation if it is monotonically increasing.

What is the relationship between Riemann sum and integral?

Definite integrals represent the exact area under a given curve, and Riemann sums are used to approximate those areas. However, if we take Riemann sums with infinite rectangles of infinitely small width (using limits), we get the exact area, i.e. the definite integral! Created by Sal Khan.

What do Riemann sums represent?

A Riemann sum is an approximation of a region’s area, obtained by adding up the areas of multiple simplified slices of the region. It is applied in calculus to formalize the method of exhaustion, used to determine the area of a region. This process yields the integral, which computes the value of the area exactly.

Is right Riemann sum overestimate or underestimate?

If f is increasing, then its minimum will always occur on the left side of each interval, and its maximum will always occur on the right side of each interval. So for increasing functions, the left Riemann sum is always an underestimate and the right Riemann sum is always an overestimate.

What is monotonic relationship?

A monotonic relationship is a relationship that does one of the following: (1) as the value of one variable increases, so does the value of the other variable, OR, (2) as the value of one variable increases, the other variable value decreases.

How do you know if a Riemann sum is overestimate or underestimate?

If the graph is increasing on the interval, then the left-sum is an underestimate of the actual value and the right-sum is an overestimate. If the curve is decreasing then the right-sums are underestimates and the left-sums are overestimates.

How do you know if a Riemann sum is an overestimate or underestimate?

What is underestimate and overestimate in math?

When the estimate is higher than the actual value, it’s called an overestimate. When the estimate is lower than the actual value, it’s called an underestimate.