Calculus Examples

$2 \sin (x)$

Step 1

Write $2 \sin (x)$ as a function.

$f (x) = 2 \sin (x)$

Step 2

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

$F (x) = \int 2 \sin (x) d x$

Step 4

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int \sin (x) d x$

Step 5

The integral of $\sin (x)$ with respect to $x$ is $- \cos (x)$ .

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

Step 6

Simplify the answer.

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Step 6.1

Simplify.

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

Step 6.2

Multiply $- 1$ by $2$ .

$- 2 \cos (x) + C$

Step 7

The answer is the antiderivative of the function $f (x) = 2 \sin (x)$ .

$F (x) =$ $- 2 \cos (x) + C$