## Related questions with answers

Question

Find all the antiderivatives of the following function. Check your work by taking derivatives. f(x) = 2 sin x + 1

Solution

VerifiedStep 1

1 of 2A function $F$ is and antiderivative of $f$ on an interval $I$ provided $F'(x)=f(x)$, for all $x$ in $I$.

In our case, we have $f(x)=2\sin(x)+1$. We have to find $F(x)$, such that $F'(x)=f(x)$. Therefore,

$\begin{gather*} F(x)=-2\cos(x)+x+C \end{gather*}$

To verify, we calculate $F'(x)$.

$\begin{gather*} F'(x)=(-2\cos(x)+x+C)'\\ F'(x)=2\sin(x)+1\\ F'(x)=f(x) \end{gather*}$

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