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Problem

Find the most general antiderivative of the funct…

01:03

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Answered step-by-step

Problem 5 Easy Difficulty

Find the most general antiderivative of the function.
(Check your answers by differentiation.)

$ f(x) = x(12x + 8) $


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02:25

KZ

Kyle Zolkin

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Related Topics

Derivatives

Differentiation

Volume

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04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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Watch More Solved Questions in Chapter 4

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Problem 78
Problem 79

Video Transcript

So for this problem we're trying to find the anti derivative of the function that's going to be F of X equals X times 12 X plus eight. So I'm going to actually distribute that. We're going to have 12 X squared plus eight X. And it will actually make it easier in the long run because when we take the anti derivative we'll have 12 X. Cubed over three, it will be four X cubed. Then we'll have plus eight X squared over two. That'll be plus four X squared. Now that we have this, we can check it, we have to remember to add the plus C. So then um when we check this will take f crime of acts and choose any random value for C. As we change, it doesn't matter. We see the F. Prime of X is the same as the F. Of X graph. Therefore we solve this correctly.

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Related Topics

Derivatives

Differentiation

Volume

Top Calculus 2 / BC Educators
Grace He

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Anna Marie Vagnozzi

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Lectures

Video Thumbnail

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Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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