Problem

Find the most general antiderivative of the funct…

02:29

Problem 6 Medium Difficulty

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

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

Answer

$\frac{x^{3}}{3}-5 x^{2}+25 x+C$

Discussion

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Video Transcript

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.

Carson M.

California Baptist University

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Problem