What is the integral of 4/pi sin((pix)/4) ?

The integral of 4/pi sin((pix)/4) is -(16}{pi^2}cos(\frac{pix)/4)+C

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integral of 4/pi sin((pix)/4)

\int \frac{4}{π} sin (\frac{π x}{4}) d x

- \frac{16}{π ^{2}} cos (\frac{π x}{4}) + C

Solution steps

\int \frac{4}{π} sin (\frac{π x}{4}) d x

Take the constant out:

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

= \frac{4}{π} \cdot \int sin (\frac{π x}{4}) d x

Apply u-substitution

: \int sin (u) \frac{4}{π} d u

= \frac{4}{π} \cdot \int sin (u) \frac{4}{π} d u

Take the constant out:

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

= \frac{4}{π} \cdot \frac{4}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{4}{π} \cdot \frac{4}{π} (- cos (u))

Substitute back

u = \frac{π x}{4}

= \frac{4}{π} \cdot \frac{4}{π} (- cos (\frac{π x}{4}))

Simplify

\frac{4}{π} \cdot \frac{4}{π} (- cos (\frac{π x}{4})) : - \frac{16}{π ^{2}} cos (\frac{π x}{4})

= - \frac{16}{π ^{2}} cos (\frac{π x}{4})

Add a constant to the solution

= - \frac{16}{π ^{2}} cos (\frac{π x}{4}) + C

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What is the integral of 4/pi sin((pix)/4) ?
The integral of 4/pi sin((pix)/4) is -(16}{pi^2}cos(\frac{pix)/4)+C