Calculus Examples

$\frac{d A}{d t} = - kA$

Step 1

Rewrite the equation.

$d A = - kA d t$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d A = \int - kA d t$

Step 2.2

Apply the constant rule.

$A + C_{1} = \int - kA d t$

Step 2.3

Integrate the right side.

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Step 2.3.1

Apply the constant rule.

$A + C_{1} = - kA t + C_{2}$

Step 2.3.2

Reorder terms.

$A + C_{1} = - t kA + C_{2}$

Step 2.4

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

$A = - t kA + K$