Question

question 1 - 1 point
find the most general antiderivative (including the constant term, c), f(x), of the function
f(x)=10 sin(x)-2 cos(x).
provide your answer below:
f(x)=

Explanation:

Step1: Recall antiderivative rules

The antiderivative of $\sin(x)$ is $-\cos(x)$ and of $\cos(x)$ is $\sin(x)$.

Step2: Find antiderivative of each term

For the term $10\sin(x)$, its antiderivative is $10\times(-\cos(x))=- 10\cos(x)$. For the term $-2\cos(x)$, its antiderivative is $-2\sin(x)$.

Step3: Add the constant of integration

The most general antiderivative $F(x)$ of $f(x)$ is the sum of the antiderivatives of its terms plus a constant $C$. So $F(x)=-10\cos(x)-2\sin(x)+C$.

Answer:

$-10\cos(x)-2\sin(x)+C$