Calculus Examples

$\int_{0}^{π} 2 \cos (x) d x$

Step 1

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int_{0}^{π} \cos (x) d x$

Step 2

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

$2 (\sin (x)]_{0}^{π})$

Step 3

Simplify the answer.

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Step 3.1

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

$2 (\sin (π) - \sin (0))$

Step 3.2

Simplify.

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Step 3.2.1

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

$2 (\sin (π) - 0)$

Step 3.2.2

Multiply $- 1$ by $0$ .

$2 (\sin (π) + 0)$

Step 3.2.3

Add $\sin (π)$ and $0$ .

$2 \sin (π)$

Step 3.3

Simplify.

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Step 3.3.1

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

$2 \sin (0)$

Step 3.3.2

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

$2 \cdot 0$

Step 3.3.3

Multiply $2$ by $0$ .

$0$