Calculus Examples

$\int_{0}^{π} 10 \sin (x) d x$

Step 1

Since $10$ is constant with respect to $x$ , move $10$ out of the integral.

$10 \int_{0}^{π} \sin (x) d x$

Step 2

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

$10 (- \cos (x)]_{0}^{π})$

Step 3

Simplify the answer.

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Step 3.1

Evaluate $- \cos (x)$ at $π$ and at $0$ .

$10 (- \cos (π) + \cos (0))$

Step 3.2

The exact value of $\cos (0)$ is $1$ .

$10 (- \cos (π) + 1)$

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. Make the expression negative because cosine is negative in the second quadrant.

$10 (- - \cos (0) + 1)$

Step 3.3.2

The exact value of $\cos (0)$ is $1$ .

$10 (- (- 1 \cdot 1) + 1)$

Step 3.3.3

Multiply $- 1$ by $1$ .

$10 (- - 1 + 1)$

Step 3.3.4

Multiply $- 1$ by $- 1$ .

$10 (1 + 1)$

Step 3.3.5

Add $1$ and $1$ .

$10 \cdot 2$

Step 3.3.6

Multiply $10$ by $2$ .

$20$