Calculus Examples

$f (x) = \frac{1}{\sqrt{1 - x^{2}}}$

Step 1

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 2

Set up the integral to solve.

$F (x) = \int \frac{1}{\sqrt{1 - x^{2}}} d x$

Step 3

Rewrite $1$ as $1^{2}$ .

$\int \frac{1}{\sqrt{1^{2} - x^{2}}} d x$

Step 4

The integral of $\frac{1}{\sqrt{1^{2} - x^{2}}}$ with respect to $x$ is $\arcsin (x)$

$\arcsin (x) + C$

Step 5

The answer is the antiderivative of the function $f (x) = \frac{1}{\sqrt{1 - x^{2}}}$ .

$F (x) =$ $\arcsin (x) + C$