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Evaluate the definite integral.
$ \displaystyle \int^{\pi/4}_{-\pi/4} (x^3 + x^4 \tan x) \, dx $
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02:48
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 5
The Substitution Rule
Integration
Campbell University
University of Michigan - Ann Arbor
Idaho State University
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.
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Okay, The first thing we know we could do for this is evaluate half of negative acts, So simply plug in negative acts everywhere. Worry you would otherwise have a positive X. As you can see, the function is odd from Night of X is the same thing as negative aftereffects. Therefore, because we know due to the cemetery, we know that because it's odd, it's simply gonna be zero as our solution because we're having the same thing minus the same thing. So, for example, X minus X. Therefore, this gives us zero is our solution for the integral. So this method of cemetery is a shortcut to figure out the solution to the integral.
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