Question

find the antiderivative for each function when c equals 0.
a. ( f(x)=-11 sin (11 x) ) b. ( g(x)=8 sin (x) ) c. ( h(x)=sin (11 x)-8 sin (8 x) )
a. the antiderivative of ( -11 sin (11 x) ) is

Explanation:

Step1: Recall the antiderivative formula

The antiderivative of \(k\sin(mx)\) is \(-\frac{k}{m}\cos(mx)+C\).

Step2: Apply the formula to \(f(x)=- 11\sin(11x)\)

Here \(k = - 11\) and \(m = 11\). Substitute into the formula: \(-\frac{-11}{11}\cos(11x)+C\).
Since \(C = 0\), simplify the expression: \(\cos(11x)\).

Answer:

\(\cos(11x)\)