Calculus Examples

f (x) = x^{2} - 3

$f (x) = x^{2} - 3$

Step 1

The function

F (x)

$F (x)$ can be found by finding the indefinite integral of the derivative

f (x)

$f (x)$ .

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

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

Step 2

Set up the integral to solve.

F (x) = \int x^{2} - 3 d x

$F (x) = \int x^{2} - 3 d x$

Step 3

Split the single integral into multiple integrals.

\int x^{2} d x + \int - 3 d x

$\int x^{2} d x + \int - 3 d x$

Step 4

By the Power Rule, the integral of

x^{2}

$x^{2}$ with respect to

x

$x$ is

\frac{1}{3} x^{3}

$\frac{1}{3} x^{3}$ .

\frac{1}{3} x^{3} + C + \int - 3 d x

$\frac{1}{3} x^{3} + C + \int - 3 d x$

Step 5

Apply the constant rule.

\frac{1}{3} x^{3} + C - 3 x + C

$\frac{1}{3} x^{3} + C - 3 x + C$

Step 6

Simplify.

\frac{1}{3} x^{3} - 3 x + C

$\frac{1}{3} x^{3} - 3 x + C$

Step 7

The answer is the antiderivative of the function

f (x) = x^{2} - 3

$f (x) = x^{2} - 3$ .

F (x) =

$F (x) =$

\frac{1}{3} x^{3} - 3 x + C

$\frac{1}{3} x^{3} - 3 x + C$

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