Calculus Examples

\int_{0}^{\frac{π}{2}} \cos (x) d x

$\int_{0}^{\frac{π}{2}} \cos (x) d x$

Step 1

The integral of

\cos (x)

$\cos (x)$ with respect to

x

$x$ is

\sin (x)

$\sin (x)$ .

\sin (x)]_{0}^{\frac{π}{2}}

$\sin (x)]_{0}^{\frac{π}{2}}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate

\sin (x)

$\sin (x)$ at

\frac{π}{2}

$\frac{π}{2}$ and at

0

$0$ .

\sin (\frac{π}{2}) - \sin (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})

$\sin (\frac{π}{2})$ is

1

$1$ .

1 - \sin (0)

$1 - \sin (0)$

Step 2.2.2

The exact value of

\sin (0)

$\sin (0)$ is

0

$0$ .

1 - 0

$1 - 0$

Step 2.2.3

Multiply

- 1

$- 1$ by

0

$0$ .

1 + 0

$1 + 0$

Step 2.2.4

Add

1

$1$ and

0

$0$ .

1

$1$

1

$1$

1

$1$

\int_{0}^{\frac{π}{2}} \cos (x) d x

$\int_{0}^{\frac{π}{2}} \cos (x) d x$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$