Q:
# What Is the Midpoint Rule in Calculus?

The midpoint rule of calculus is a method for approximating the value of the area under the graph during numerical integration. This is one of several rules used for approximation during numerical integration.

Continue Reading
Credit:
Dan Moore
E+
Getty Images

The midpoint rule of calculus has several general steps. Consider a formula that takes the value y = b(x) over an interval of x1 to x2, where x2 is equal to x1 + h. The value h refers to the distance on the x-axis between the start and end points. The midpoint rule with these values is equal to hf (x1 + h/2).

There is a variation to the midpoint rule that is also used in calculus, referred to as the composite midpoint rule. This variation approximates the value of the area under the graph by summing a series of rectangles. The intervals of this variation are found by dividing the distance between x1 and x2 into equal amounts. This formula is equal to h = (x2 - x1)/m, where m is the number of subintervals.

There are several other methods of numerical integration that are used to approximate the area under the graph. The triangle and trapezoid rules both use the summation of their respective shapes under the graph to approximate the area.

Learn more about Calculus-
Q:
## What Is the Multivariable Chain Rule?

A: The multivariable chain rule is a formula in calculus used to find the derivative of the composition of multiple functions. In the multivariable chain rule... Full Answer >Filed Under: -
Q:
## What Is Chain Rule Integration?

A: The term chain rule integration refers to the integration technique that reverses the process of differentiating using the chain rule. Chain rule integrati... Full Answer >Filed Under: -
Q:
## What Is the Precise Definition of a Limit in Calculus?

A: The definition of a limit in calculus is the value that a function gets close to but never surpasses as the input changes. Limits are one of the most impor... Full Answer >Filed Under: -
Q:
## What Is the Significance of Ln 1/x in Calculus?

A: In calculus, the primary significance of 1/x is its value as the derivative of the natural logarithm of "x." The proof for the derivative of ln(x) may be f... Full Answer >Filed Under: