Calculus Examples

$\frac{d L}{d x} = - kL$

Step 1

Rewrite the equation.

$d L = - kL d x$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d L = \int - kL d x$

Step 2.2

Apply the constant rule.

$L + C_{1} = \int - kL d x$

Step 2.3

Integrate the right side.

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Step 2.3.1

Apply the constant rule.

$L + C_{1} = - kL x + C_{2}$

Step 2.3.2

Reorder terms.

$L + C_{1} = - x kL + C_{2}$

Step 2.4

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

$L = - x kL + K$