Calculus Examples

$\int_{- π}^{π} \cos (x) d x$

Step 1

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

$\sin (x)]_{- π}^{π}$

Step 2

Evaluate $\sin (x)$ at $π$ and at $- π$ .

$\sin (π) - \sin (- π)$

Step 3

Simplify.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

$\sin (0) - \sin (- π)$

Step 3.1.2

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

$0 - \sin (- π)$

Step 3.1.3

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

$0 - \sin (0)$

Step 3.1.4

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

$0 - 0$

Step 3.1.5

Multiply $- 1$ by $0$ .

$0 + 0$

Step 3.2

Add $0$ and $0$ .

$0$