Calculus Examples

$\int_{0}^{\frac{π}{4}} \cos (x) d x$

Step 1

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

$\sin (x)]_{0}^{\frac{π}{4}}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $\sin (x)$ at $\frac{π}{4}$ and at $0$ .

$\sin (\frac{π}{4}) - \sin (0)$

Step 2.2

Simplify.

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Step 2.2.1

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} - \sin (0)$

Step 2.2.2

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

$\frac{\sqrt{2}}{2} - 0$

Step 2.2.3

Multiply $- 1$ by $0$ .

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

Step 2.2.4

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

$\frac{\sqrt{2}}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2}}{2}$

Decimal Form:

$0.70710678 \dots$