Calculus Examples

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

Step 1

Rewrite the equation.

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

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

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

Step 2.2

Apply the constant rule.

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

Step 2.3

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

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

Step 2.4

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

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