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Write as a single integral in the form $ \displaystyle \int^b_a f(x) \, dx $:

$$ \int^2_{-2} f(x) \, dx + \int^5_2 f(x) \, dx - \int^{-1}_{-2} f(x) \, dx $$

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$\int_{-1}^{5} f(x) d x$

00:56

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

Campbell University

Harvey Mudd College

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.

04:12

Write as a single integral…

02:17

02:12

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01:16

00:54

Express as one integral.

00:27

00:43

01:02

express each integral as a…

Okay. The first thing you know we can do is we can write the interval from negative to five affects DX minus the integral from negative to the night of one after Rex detox. As as you can see, we're splitting it up. It's We can cancel. We can cancel these two. They have the same bounds. Giving us the integral from negative 1 to 5 affects DX was our solution.

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