Calculus Examples

$\int_{\frac{π}{6}}^{\frac{π}{2}} \cos (x) d x$

Step 1

The integral of $\cos (x)$ with respect to $x$ is $\sin (x)$ .

$\sin (x)]_{\frac{π}{6}}^{\frac{π}{2}}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $\sin (x)$ at $\frac{π}{2}$ and at $\frac{π}{6}$ .

$\sin (\frac{π}{2}) - \sin (\frac{π}{6})$

Step 2.2

Simplify.

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Step 2.2.1

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$1 - \sin (\frac{π}{6})$

Step 2.2.2

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$1 - \frac{1}{2}$

Step 2.2.3

Write $1$ as a fraction with a common denominator.

$\frac{2}{2} - \frac{1}{2}$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{2 - 1}{2}$

Step 2.2.5

Subtract $1$ from $2$ .

$\frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$