Calculus Examples

$\frac{d P}{d t} = k \sqrt[3]{p}$

Step 1

Rewrite the equation.

$d P = k \sqrt[3]{p} d t$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d P = \int k \sqrt[3]{p} d t$

Step 2.2

Apply the constant rule.

$P + C_{1} = \int k \sqrt[3]{p} d t$

Step 2.3

Integrate the right side.

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Step 2.3.1

Apply the constant rule.

$P + C_{1} = k \sqrt[3]{p} t + C_{2}$

Step 2.3.2

Reorder terms.

$P + C_{1} = k t \sqrt[3]{p} + C_{2}$

Step 2.4

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

$P = k t \sqrt[3]{p} + K$