Calculus Examples

$\int_{0}^{\frac{π}{2}} \cot (x) d x$

Step 1

The integral of $\cot (x)$ with respect to $x$ is $\ln (| \sin (x) |)$ .

$\ln (| \sin (x) |)]_{0}^{\frac{π}{2}}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $\ln (| \sin (x) |)$ at $\frac{π}{2}$ and at $0$ .

$\ln (| \sin (\frac{π}{2}) |) - \ln (| \sin (0) |)$

Step 2.2

Simplify.

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Step 2.2.1

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

$\ln (| 1 |) - \ln (| \sin (0) |)$

Step 2.2.2

The exact value of $\sin (0)$ is $0$ .

$\ln (| 1 |) - \ln (| 0 |)$

Step 2.2.3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{| 1 |}{| 0 |})$

Step 2.3

Simplify.

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Step 2.3.1

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$\ln (\frac{| 1 |}{0})$

Step 2.3.2

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\ln (\frac{| 1 |}{0})$

Step 2.4

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\ln (\frac{| 1 |}{0})$

Step 3

The expression contains a division by $0$ . The expression is undefined.

Undefined