Calculus Examples

$d y = x^{2} d x$

Step 1

Set up an integral on each side.

$\int d y = \int x^{2} d x$

Step 2

Apply the constant rule.

$y + C_{1} = \int x^{2} d x$

Step 3

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

$y + C_{1} = \frac{1}{3} x^{3} + C_{2}$

Step 4

Group the constant of integration on the right side as $K$ .

$y = \frac{1}{3} x^{3} + K$