Calculus Examples

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

Step 1

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

$- \cos (x)]_{\frac{π}{3}}^{\frac{π}{2}}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $- \cos (x)$ at $\frac{π}{2}$ and at $\frac{π}{3}$ .

$- \cos (\frac{π}{2}) + \cos (\frac{π}{3})$

Step 2.2

Simplify.

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Step 2.2.1

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$- 0 + \cos (\frac{π}{3})$

Step 2.2.2

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$- 0 + \frac{1}{2}$

Step 2.2.3

Multiply $- 1$ by $0$ .

$0 + \frac{1}{2}$

Step 2.2.4

Add $0$ and $\frac{1}{2}$ .

$\frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$