Calculus Examples

$\int_{0}^{2 π} \cos (x) d x$

Step 1

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

$\sin (x)]_{0}^{2 π}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $\sin (x)$ at $2 π$ and at $0$ .

$\sin (2 π) - \sin (0)$

Step 2.2

Simplify.

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Step 2.2.1

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

$\sin (2 π) - 0$

Step 2.2.2

Multiply $- 1$ by $0$ .

$\sin (2 π) + 0$

Step 2.2.3

Add $\sin (2 π)$ and $0$ .

$\sin (2 π)$

Step 3

Simplify.

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Step 3.1

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

$\sin (0)$

Step 3.2

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

$0$