Calculus Examples

$\sqrt{2} \cos (x)$

Step 1

Write $\sqrt{2} \cos (x)$ as a function.

$f (x) = \sqrt{2} \cos (x)$

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.

$F (x) = \int \sqrt{2} \cos (x) d x$

Step 4

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

$\sqrt{2} \int \cos (x) d x$

Step 5

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

$\sqrt{2} (\sin (x) + C)$

Step 6

Simplify.

$\sqrt{2} \sin (x) + C$

Step 7

The answer is the antiderivative of the function $f (x) = \sqrt{2} \cos (x)$ .

$F (x) =$ $\sqrt{2} \sin (x) + C$