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Find complete families of polynomial anti-derivatives

Question 1 of 8

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Check an anti-derivative by differentiating your result

g(u)=9u^{2}

Find the complete family of anti-derivatives, including one arbitrary constant C

(a)4 marks

P denotes the anti-derivative with zero constant term. Enter 0 for its constant coefficient

Enter every coefficient in descending powers, including zero for an absent term

P(u)=A_3u^{3}+A_2u^{2}+A_1u+A_0

\(\text{coefficient of }u^{3}\) \(\text{coefficient of }u^{2}\) \(\text{coefficient of }u\) \(\text{constant coefficient}\)

(b)1 mark

Select the complete family. C denotes an arbitrary real constant

F(u)=3u^{3}+C

F(u)=9u^{2}+C

F(u)=3u^{3}

F(u)=-3u^{3}+C

Enter the highest power in the anti-derivative polynomial

Exact value