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Using the middle point with $n=4,$ approximate the area of the region bounded by $f(x)=4-x^{2},$ and the $x$ -axis for $x$ between -2 and $2,$ see Figure 19.

11

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 4

Approximation of Areas

Integrals

Missouri State University

Harvey Mudd College

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

02:50

Use the Midpoint Rule with…

03:00

03:19

02:12

03:15

03:26

02:11

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