Calculus Examples

$\int_{n π}^{(n + 2) π} 9 \cos (x) d x$

Step 1

Since $9$ is constant with respect to $x$ , move $9$ out of the integral.

$9 \int_{n π}^{(n + 2) π} \cos (x) d x$

Step 2

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

$9 (\sin (x)]_{n π}^{(n + 2) π})$

Step 3

Evaluate $\sin (x)$ at $(n + 2) π$ and at $n π$ .

$9 (\sin ((n + 2) π) - \sin (n π))$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$9 (\sin (n π + 2 π) - \sin (n π))$

Step 4.2

Apply the distributive property.

$9 \sin (n π + 2 π) + 9 (- \sin (n π))$

Step 4.3

Multiply $- 1$ by $9$ .

$9 \sin (n π + 2 π) - 9 \sin (n π)$