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Evaluate the integral and interpret it as a difference of areas. Illustrate with a sketch.

$ \displaystyle \int^2_{-1} x^3 \,dx $

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00:49

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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.

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Evaluate the integrals. Sk…

Okay. We know the intro from negative 1 to 2 of X cube De axe is X to the fourth divide by four. From negative one too. Plug in. This is the area over here of this region in this the area of this region and we know is we saw our solution is 15 over four.

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