Calculus Examples

$\int_{0}^{π} 2 \sin (x) d x$

Step 1

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int_{0}^{π} \sin (x) d x$

Step 2

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

$2 (- \cos (x)]_{0}^{π})$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Evaluate $- \cos (x)$ at $π$ and at $0$ .

$2 (- \cos (π) + \cos (0))$

Step 3.2

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

$2 (- \cos (π) + 1)$

Step 3.3

Simplify.

Tap for more steps...

Step 3.3.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$2 (- - \cos (0) + 1)$

Step 3.3.2

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

$2 (- (- 1 \cdot 1) + 1)$

Step 3.3.3

Multiply $- 1$ by $1$ .

$2 (- - 1 + 1)$

Step 3.3.4

Multiply $- 1$ by $- 1$ .

$2 (1 + 1)$

Step 3.3.5

Add $1$ and $1$ .

$2 \cdot 2$

Step 3.3.6

Multiply $2$ by $2$ .

$4$