Calculus Examples

$\int_{0}^{\frac{π}{3}} 4 \sec (x) \tan (x) d x$

Step 1

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$4 \int_{0}^{\frac{π}{3}} \sec (x) \tan (x) d x$

Step 2

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

$4 (\sec (x)]_{0}^{\frac{π}{3}})$

Step 3

Simplify the answer.

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Step 3.1

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

$4 (\sec (\frac{π}{3}) - \sec (0))$

Step 3.2

Simplify.

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Step 3.2.1

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

$4 (2 - \sec (0))$

Step 3.2.2

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

$4 (2 - 1 \cdot 1)$

Step 3.2.3

Multiply $- 1$ by $1$ .

$4 (2 - 1)$

Step 3.2.4

Subtract $1$ from $2$ .

$4 \cdot 1$

Step 3.2.5

Multiply $4$ by $1$ .

$4$