Calculus Examples

$\int_{0}^{\frac{π}{6}} 4 \cos (x) d x$

Step 1

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$4 \int_{0}^{\frac{π}{6}} \cos (x) d x$

Step 2

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

$4 (\sin (x)]_{0}^{\frac{π}{6}})$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Evaluate $\sin (x)$ at $\frac{π}{6}$ and at $0$ .

$4 (\sin (\frac{π}{6}) - \sin (0))$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

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

$4 (\frac{1}{2} - \sin (0))$

Step 3.2.2

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

$4 (\frac{1}{2} - 0)$

Step 3.2.3

Multiply $- 1$ by $0$ .

$4 (\frac{1}{2} + 0)$

Step 3.2.4

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

$4 (\frac{1}{2})$

Step 3.2.5

Combine $4$ and $\frac{1}{2}$ .

$\frac{4}{2}$

Step 3.2.6

Cancel the common factor of $4$ and $2$ .

Tap for more steps...

Step 3.2.6.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 2}{2}$

Step 3.2.6.2

Cancel the common factors.

Tap for more steps...

Step 3.2.6.2.1

Factor $2$ out of $2$ .

$\frac{2 \cdot 2}{2 (1)}$

Step 3.2.6.2.2

Cancel the common factor.

$\frac{2 \cdot 2}{2 \cdot 1}$

Step 3.2.6.2.3

Rewrite the expression.

$\frac{2}{1}$

Step 3.2.6.2.4

Divide $2$ by $1$ .

$2$