find the antiderivative for each function when c equals 0. a. f(x)= - 6 sin (6x) b. g(x)=5 sin (x) c…

Explanation:

Step1: Recall antiderivative formula

The antiderivative of $\sin(ax)$ is $-\frac{1}{a}\cos(ax)+C$. Here $a = 6$ and the function is $- 6\sin(6x)$.

Step2: Apply the formula

For $y=-6\sin(6x)$, the antiderivative $F(x)=-6\times\left(-\frac{1}{6}\right)\cos(6x)$.

Step3: Simplify the result

$F(x)=\cos(6x)$ since $-6\times\left(-\frac{1}{6}\right) = 1$ and $C = 0$.

Answer:

$\cos(6x)$