Calculus Examples

$\int_{0}^{\frac{π}{3}} \sec (x) \tan (x) d x$

Step 1

Since the derivative of $\sec (x)$ is $\sec (x) \tan (x)$ , the integral of $\sec (x) \tan (x)$ is $\sec (x)$ .

$\sec (x)]_{0}^{\frac{π}{3}}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $\sec (x)$ at $\frac{π}{3}$ and at $0$ .

$\sec (\frac{π}{3}) - \sec (0)$

Step 2.2

Simplify.

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Step 2.2.1

The exact value of $\sec (\frac{π}{3})$ is $2$ .

$2 - \sec (0)$

Step 2.2.2

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

$2 - 1 \cdot 1$

Step 2.2.3

Multiply $- 1$ by $1$ .

$2 - 1$

Step 2.2.4

Subtract $1$ from $2$ .

$1$