Question

find all the antiderivatives of the following function. f(x)=2 sin x - 4 the antiderivatives of f(x)=2 sin x - 4 are f(x)=□

Explanation:

Step1: Recall antiderivative rules

The antiderivative of $\sin x$ is $-\cos x$ and of a constant $a$ is $ax$.

Step2: Find antiderivative of each term

For the term $2\sin x$, its antiderivative is $2\times(-\cos x)= - 2\cos x$. For the term $-4$, its antiderivative is $-4x$.

Step3: Add the constant of integration

The general antiderivative of a function has an arbitrary constant $C$. So the antiderivative of $f(x)=2\sin x - 4$ is $F(x)=-2\cos x-4x + C$.

Answer:

$-2\cos x-4x + C$