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Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take $ C = 0 $).

$ \displaystyle \int \sin x \cos^4 x \, dx $

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$-\frac{\cos ^{5} x}{5}+C$

01:16

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

01:26

Evaluate the indefinite in…

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Okay. The first thing we know is that you is co sign axe, which means that negative d'you is equivalent to sign acts. DX won't take the drug, but everyone transfer the negative over to the left hand side. Over here is you could see which means this is equivalent to the integral negative times the integral of you to the fourth d'you using the power ruled. This means we increase the expletive by 125 divided by the expert at five back substitute end co sign. Okay, Now we are at the point where we can grass and it continues on words like that. As you can seek, the answer is reasonable because we can see the graph of f is zero in capital F has a local extreme A. We see its negative when we see it's decreasing in positive months, increasing

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