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

$ f(x) = (x - 5)^2 $

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02:41

Kyle Zolkin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Boston College

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 here were given the function F of X equals x minus five squared. But I would advise that you foil this. So that would give you X squared minus 10. It's plus 25. And the reason why I advise this is because now you have three separate terms that you can take the anti derivative of rather than having um some power involved with parentheses in terms inside. So this makes it much simpler. And now we want to find the anti derivative. So this is going to give us X cubed over three, is going to give us a negative 10 X squared over two, which is negative five X squared. And then 25 a constant is just gonna give us 25 x. Then we add the constancy at the end of this. Then we can take crime effects with any constancy. And we see that it's the same graph as the original fx function. So we solve this correctly.

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