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Use the properties about odd and even functions to evaluate the given integral.$$\int_{-4}^{4}\left(3 x^{2}+1\right)\left(2 x^{3}+2 x\right)^{5} d x$$

$$0$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 7

Substitution and Properties of Definite Integrals

Integrals

Oregon State University

University of Nottingham

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.

02:54

Use the properties about o…

02:07

01:35

00:36

Evaluate the integral usin…

00:50

01:31

Write the integral as the …

02:19

Find $\int_{2}^{5} f(x) d …

01:12

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