Calculus Examples

$\frac{d x}{d t} = t$

Step 1

Rewrite the equation.

$d x = t d t$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d x = \int t d t$

Step 2.2

Apply the constant rule.

$x + C_{1} = \int t d t$

Step 2.3

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

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

Step 2.4

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

$x = \frac{1}{2} t^{2} + K$