Calculus Examples

$\int_{0}^{\frac{π}{2}} \cos (x) d x$

Step 1

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

$\sin (x)]_{0}^{\frac{π}{2}}$

Step 2

Simplify the answer.

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Step 2.1

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

$\sin (\frac{π}{2}) - \sin (0)$

Step 2.2

Simplify.

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Step 2.2.1

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

$1 - \sin (0)$

Step 2.2.2

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

$1 - 0$

Step 2.2.3

Multiply $- 1$ by $0$ .

$1 + 0$

Step 2.2.4

Add $1$ and $0$ .

$1$