Calculus Examples

$\int_{0}^{\frac{π}{2}} 3 \cos (x) d x$

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int_{0}^{\frac{π}{2}} \cos (x) d x$

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

$3 (\sin (x)]_{0}^{\frac{π}{2}})$

Simplify the answer.

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

$3 (\sin (\frac{π}{2}) - \sin (0))$

Simplify.

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The exact value of $\sin (\frac{π}{2})$ is $1$ .

$3 (1 - \sin (0))$

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

$3 (1 - 0)$

Multiply $- 1$ by $0$ .

$3 (1 + 0)$

Add $1$ and $0$ .

$3 \cdot 1$

Multiply $3$ by $1$ .

$3$