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How do you find the most general antiderivative of the function #f(x) = x(8 - x)^2#?

Answer 1

Elijah Abram

#f(x) = x(8 - x)^2# multiply it out to get standard form for a polynomial, then antidifferentiate term by term.

#f(x) = x(8 - x)^2 = x(64-16x+x^2) = x^3 - 16x^2+ 64x#

Whose antiderivative is: #1/4 x^4 - 16/3 x^3 +32 x^2 + C#

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Answer 2

Charles Arocha

To find the most general antiderivative of the function ( f(x) = x(8 - x)^2 ), you can integrate it with respect to ( x ) using the integration techniques such as substitution or expanding and simplifying the expression. After integration, you will get the antiderivative of the function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.