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Evaluate the indefinite integral.

$ \displaystyle \int x \sqrt{1 - x^2} \, dx $

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$-\frac{1}{3}\left(1-x^{2}\right)^{3 / 2}+C$

01:47

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Oregon State University

Harvey Mudd College

University of Nottingham

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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Okay, We've been given this problem that you is one highest explored. Take the derivative. In other words, do you? We got negative two ex DX, which means writing this in terms of x t X. We have negative 1/2 to you. Okay, Now I'm taking the integral. We know we can pull the constant negative half out. Use the power all for integration, which is increased the explain it by one divide by the new X Poona Now back substitute. And because we don't want you in our final solution and we have our integral

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