Calculus Examples

$\int_{\frac{π}{4}}^{\frac{π}{3}} \sec^{2} (x) d x$

Step 1

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

$\tan (x)]_{\frac{π}{4}}^{\frac{π}{3}}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $\tan (x)$ at $\frac{π}{3}$ and at $\frac{π}{4}$ .

$\tan (\frac{π}{3}) - \tan (\frac{π}{4})$

Step 2.2

Simplify.

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Step 2.2.1

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

$\sqrt{3} - \tan (\frac{π}{4})$

Step 2.2.2

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$\sqrt{3} - 1 \cdot 1$

Step 2.2.3

Multiply $- 1$ by $1$ .

$\sqrt{3} - 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3} - 1$

Decimal Form:

$0.73205080 \dots$