Calculus Examples

$\int_{0}^{\frac{π}{4}} \sin (x) d x$

Step 1

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

$- \cos (x)]_{0}^{\frac{π}{4}}$

Step 2

Simplify the answer.

Tap for more steps...

Step 2.1

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

$- \cos (\frac{π}{4}) + \cos (0)$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

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

$- \frac{\sqrt{2}}{2} + \cos (0)$

Step 2.2.2

The exact value of $\cos (0)$ is $1$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.29289321 \dots$