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

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

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02:25

Kyle Zolkin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:35

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.

06:14

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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Find the most general anti…

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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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