Calculus Examples

$1 - x$

Step 1

Split the single integral into multiple integrals.

$\int d x + \int - x d x$

Step 2

Apply the constant rule.

$x + C + \int - x d x$

Step 3

Since $- 1$ is constant with respect to $x$ , move $- 1$ out of the integral.

$x + C - \int x d x$

Step 4

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$x + C - (\frac{1}{2} x^{2} + C)$

Step 5

Simplify.

$x - \frac{1}{2} x^{2} + C$