Find the antiderivative of f'(x)=3x^3?

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Find the antiderivative of f'(x)=3x^3?

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Answer 1 · 2018-02-26T20:54:24

$\frac{3}{4} x^{4} + C$ $3/4 x^4 +C$

Explanation:

When differentiation $a x^{b}$ $ax^b$ you multiply the coefficient of the x term by the power and then reduce the power by 1. In this case $a b x^{b - 1}$ $ab x^(b-1)$ .

An antiderivative is the opposite of this to increase the power by 1 and then divide the coefficient by the new power. So for your example, that would be $\frac{3}{4} x^{4}$ $3/4 x^4$ . However, we do not know if there was a constant when integrating (another name for antiderivative) so we write $+ C$ $+C$

Answer 2 · 2018-02-26T21:15:09

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Explanation:

The anti power rule states that:

$\int x^{n} d x = \frac{x^{n + 1}}{n + 1}$ $intx^ndx=x^(n+1)/(n+1)$

Therefore, $\int 3 x^{3} d x$ $int3x^3dx$ is:

$\frac{3 x^{3 + 1}}{3 + 1} \Rightarrow \frac{3 x^{4}}{4} + C$ $(3x^(3+1))/(3+1)=>(3x^4)/4+C$

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Find the antiderivative of f'(x)=3x^3?

I don't even know where to start

2 Answers

Explanation:

Explanation:

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