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Evaluate the integral.

$ \displaystyle \int^2_{-2} f(x) \,dx $ where $ f(x) = \left\{ \begin{array}{ll} 2 & \mbox{if $ -2 \le x \le 0 $}\\ 4 - x^2 & \mbox{if $ 0 < x \le 2 $} \end{array} \right.$

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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

Baylor University

Idaho State University

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 integral. Int…

okay. We know property of inter girls is that we can split thumb. So we're splitting into two dear ax plus four minus x squared DX. Which means now we can take the integral plug in only end up with 28 divided by three.

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