What is the integral of-2/pi cos(pi/2 x) ?

The integral of-2/pi cos(pi/2 x) is -4/(pi^2)sin((pix)/2)+C

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integral of-2/pi cos(pi/2 x)

\int - \frac{2}{π} cos (\frac{π}{2} x) d x

- \frac{4}{π ^{2}} sin (\frac{π x}{2}) + C

Solution steps

\int - \frac{2}{π} cos (\frac{π}{2} x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{2}{π} \cdot \int cos (\frac{π}{2} x) d x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{2}{π} \cdot \int cos (\frac{π x}{2}) d x

Apply u-substitution

: \int cos (u) \frac{2}{π} d u

= - \frac{2}{π} \cdot \int cos (u) \frac{2}{π} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{2}{π} \cdot \frac{2}{π} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= - \frac{2}{π} \cdot \frac{2}{π} sin (u)

Substitute back

u = \frac{π x}{2}

= - \frac{2}{π} \cdot \frac{2}{π} sin (\frac{π x}{2})

Simplify

- \frac{2}{π} \cdot \frac{2}{π} sin (\frac{π x}{2}) : - \frac{4}{π ^{2}} sin (\frac{π x}{2})

= - \frac{4}{π ^{2}} sin (\frac{π x}{2})

Add a constant to the solution

= - \frac{4}{π ^{2}} sin (\frac{π x}{2}) + C

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What is the integral of-2/pi cos(pi/2 x) ?
The integral of-2/pi cos(pi/2 x) is -4/(pi^2)sin((pix)/2)+C