Antiderivative
The antiderivative of a function f(x) is another function F(x) such that:
f(x)=F'(x)
The most-used antiderivative is the so-called reverse power rule:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}+C[/tex]
We have to compute:
[tex]\int (12t^2+7t-5)\text{ dt}[/tex]
Separating the integrals:
[tex]\int 12t^2\text{ dt}+\int 7t\text{ dt}-\int 5\text{ dt}[/tex]
Apply the rule above:
[tex]\frac{12t^3}{3}+7\frac{t^2}{2}-5t+C[/tex]
Simplifying:
[tex]4t^3+\frac{7}{2}t^2-5t+C[/tex]
The last option is correct
