Calculus Examples

$\int_{\frac{π}{6}}^{\frac{π}{2}} \csc (t) \cdot \cot (t) d t$

Step 1

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

$- \csc (t)]_{\frac{π}{6}}^{\frac{π}{2}}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $- \csc (t)$ at $\frac{π}{2}$ and at $\frac{π}{6}$ .

$- \csc (\frac{π}{2}) + \csc (\frac{π}{6})$

Step 2.2

Simplify.

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Step 2.2.1

The exact value of $\csc (\frac{π}{2})$ is $1$ .

$- 1 \cdot 1 + \csc (\frac{π}{6})$

Step 2.2.2

The exact value of $\csc (\frac{π}{6})$ is $2$ .

$- 1 \cdot 1 + 2$

Step 2.2.3

Multiply $- 1$ by $1$ .

$- 1 + 2$

Step 2.2.4

Add $- 1$ and $2$ .

$1$