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Evaluate the integral by making the given substitution.

$ \displaystyle \int \sin^2 \theta \cos \theta \, d\theta $, $ u = \sin \theta $

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00:58

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Missouri State University

Oregon State University

Harvey Mudd 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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02:01

okay. We know he can substitute Sign. Fada is equivalent to you. And then we know we can differentiate getting us. Do you this Cho sun that, uh, times d theta which gives us the integral of you squirt. D'You is powerful increased. Explain it by one divide by the new exponents. Now substitute end because obviously we don't want you in our final answer. And this is our solution.

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