Calculus Examples

$\int 100 - x^{2} d x$

Step 1

Split the single integral into multiple integrals.

$\int 100 d x + \int - x^{2} d x$

Step 2

Apply the constant rule.

$100 x + C + \int - x^{2} d x$

Step 3

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

$100 x + C - \int x^{2} d x$

Step 4

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$100 x + C - (\frac{1}{3} x^{3} + C)$

Step 5

Simplify.

$100 x - \frac{1}{3} x^{3} + C$