Calculus Examples

$\int_{0}^{\frac{π}{2}} \tan (x) d x$

Step 1

The integral of $\tan (x)$ with respect to $x$ is $\ln (| \sec (x) |)$ .

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

Step 2

Simplify the answer.

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Step 2.1

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

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

Step 2.2

Simplify.

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Step 2.2.1

The exact value of $\sec (0)$ is $1$ .

$\ln (| \sec (\frac{π}{2}) |) - \ln (| 1 |)$

Step 2.2.2

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

$\ln (\frac{| \sec (\frac{π}{2}) |}{| 1 |})$

Step 2.3

Simplify.

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Step 2.3.1

Rewrite $\sec (\frac{π}{2})$ in terms of sines and cosines.

$\ln (\frac{| \frac{1}{\cos (\frac{π}{2})} |}{| 1 |})$

Step 2.3.2

The exact value of $\cos (\frac{π}{2})$ is $0$ .

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

Step 2.3.3

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

Undefined

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

Step 2.4

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

Undefined

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

Step 3

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

Undefined