Calculus Examples

$\int_{0}^{\frac{π}{3}} 5 \sec^{2} (x) d x$

Step 1

Since $5$ is constant with respect to $x$ , move $5$ out of the integral.

$5 \int_{0}^{\frac{π}{3}} \sec^{2} (x) d x$

Step 2

Since the derivative of $\tan (x)$ is $\sec^{2} (x)$ , the integral of $\sec^{2} (x)$ is $\tan (x)$ .

$5 (\tan (x)]_{0}^{\frac{π}{3}})$

Step 3

Simplify the answer.

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Step 3.1

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

$5 (\tan (\frac{π}{3}) - \tan (0))$

Step 3.2

Simplify.

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Step 3.2.1

The exact value of $\tan (\frac{π}{3})$ is $\sqrt{3}$ .

$5 (\sqrt{3} - \tan (0))$

Step 3.2.2

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

$5 (\sqrt{3} - 0)$

Step 3.2.3

Multiply $- 1$ by $0$ .

$5 (\sqrt{3} + 0)$

Step 3.2.4

Add $\sqrt{3}$ and $0$ .

$5 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{3}$

Decimal Form:

$8.66025403 \dots$