Calculus Examples

$\frac{d s}{d t} = \csc^{2} (t)$

Step 1

Rewrite the equation.

$d s = \csc^{2} (t) d t$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d s = \int \csc^{2} (t) d t$

Step 2.2

Apply the constant rule.

$s + C_{1} = \int \csc^{2} (t) d t$

Step 2.3

Since the derivative of $- \cot (t)$ is $\csc^{2} (t)$ , the integral of $\csc^{2} (t)$ is $- \cot (t)$ .

$s + C_{1} = - \cot (t) + C_{2}$

Step 2.4

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

$s = - \cot (t) + K$