Calculus Examples

$\int_{0}^{1 π} \frac{19}{2} \cdot \cos (x) d x$

Step 1

Since $\frac{19}{2}$ is constant with respect to $x$ , move $\frac{19}{2}$ out of the integral.

$\frac{19}{2} \int_{0}^{1 π} \cos (x) d x$

Step 2

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

$\frac{19}{2} \sin (x)]_{0}^{1 π}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Substitute and simplify.

Tap for more steps...

Step 3.1.1

Evaluate $\sin (x)$ at $1 π$ and at $0$ .

$\frac{19}{2} ((\sin (1 π)) - \sin (0))$

Step 3.1.2

Multiply $π$ by $1$ .

$\frac{19}{2} (\sin (π) - \sin (0))$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

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

$\frac{19}{2} (\sin (π) - 0)$

Step 3.2.2

Multiply $- 1$ by $0$ .

$\frac{19}{2} (\sin (π) + 0)$

Step 3.2.3

Add $\sin (π)$ and $0$ .

$\frac{19}{2} \sin (π)$

Step 3.2.4

Combine $\frac{19}{2}$ and $\sin (π)$ .

$\frac{19 \sin (π)}{2}$

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.

$\frac{19 \sin (0)}{2}$

Step 3.3.2

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

$\frac{19 \cdot 0}{2}$

Step 3.3.3

Multiply $19$ by $0$ .

$\frac{0}{2}$

Step 3.3.4

Reduce the expression $\frac{0}{2}$ by cancelling the common factors.

Tap for more steps...

Step 3.3.4.1

Factor $2$ out of $0$ .

$\frac{2 (0)}{2}$

Step 3.3.4.2

Factor $2$ out of $2$ .

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

Step 3.3.4.3

Cancel the common factor.

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

Step 3.3.4.4

Rewrite the expression.

$\frac{0}{1}$

Step 3.3.5

Divide $0$ by $1$ .

$0$