Calculus Examples

$\int_{6 π}^{7 π} \cos (x) d x$

Step 1

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

$\sin (x)]_{6 π}^{7 π}$

Step 2

Evaluate $\sin (x)$ at $7 π$ and at $6 π$ .

$\sin (7 π) - \sin (6 π)$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sin (π) - \sin (6 π)$

Step 3.1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (0) - \sin (6 π)$

Step 3.1.3

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

$0 - \sin (6 π)$

Step 3.1.4

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$0 - \sin (0)$

Step 3.1.5

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

$0 - 0$

Step 3.1.6

Multiply $- 1$ by $0$ .

$0 + 0$

Step 3.2

Add $0$ and $0$ .

$0$