Find the most general antiderivative of the function. $f(x)=15 x^{2}-16 x+9$
A) $F(x)=5 x^{3}-8 x^{2}+9 x+C$
B) $F(x)=6 x^{2}-14 x+C$
C) $F(x)=36 x-14+C$
D) $F(x)=30 x^{5}-28 x^{4}+9 x+C$
E) $F(x)=18 x^{3}-14 x^{2}+9 x+C$

Question

Quizplus · Accepted Answer

We can use the power rule of integration and sum rule to get:
$$\int 15x^2-16x+9 dx = \frac{15}{3}x^3 - \frac{16}{2}x^2 + 9x + C = 5x^3 - 8x^2 + 9x + C$$
where C is the constant of integration. Thus, the most general antiderivative of the function is $F(x) = 5x^3 - 8x^2 + 9x + C$, which is choice (A).

Find the Most General Antiderivative of the Function f(x)=15x2−16x+9f(x)=15 x^{2}-16 x+9f(x)=15x2−16x+9

Find the Most General Antiderivative of the Function $f(x)=15 x^{2}-16 x+9$