What is the antiderivative of #f(x) = 1/2 + (3/4)x^2 - (4/5)x^3#?

Answer 1

Emilia Aguilar

#intf(x)=1/2x+1/4x^3-1/5x^4+"C"#

Using the power rule, integrating this function is straightforward:

#intax^n=(ax^(n+1))/(n+1)+"C"#

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Answer 2

Isaiah Allen

The antiderivative of ( f(x) = \frac{1}{2} + \frac{3}{4}x^2 - \frac{4}{5}x^3 ) is:

[ F(x) = \frac{1}{2}x + \frac{1}{4}x^3 - \frac{1}{5}x^4 + C ]

Where ( C ) is the constant of integration.

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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.

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