Calculus Examples

$\int_{0}^{\frac{π}{2}} 18 \sin (x) d x$

Step 1

Since $18$ is constant with respect to $x$ , move $18$ out of the integral.

$18 \int_{0}^{\frac{π}{2}} \sin (x) d x$

Step 2

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

$18 (- \cos (x)]_{0}^{\frac{π}{2}})$

Step 3

Simplify the answer.

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Step 3.1

Evaluate $- \cos (x)$ at $\frac{π}{2}$ and at $0$ .

$18 (- \cos (\frac{π}{2}) + \cos (0))$

Step 3.2

Simplify.

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Step 3.2.1

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$18 (- 0 + \cos (0))$

Step 3.2.2

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

$18 (- 0 + 1)$

Step 3.2.3

Multiply $- 1$ by $0$ .

$18 (0 + 1)$

Step 3.2.4

Add $0$ and $1$ .

$18 \cdot 1$

Step 3.2.5

Multiply $18$ by $1$ .

$18$