What is the integral of sin((pix)/6) ?

The integral of sin((pix)/6) is -6/pi cos((pix)/6)+C

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integral of sin((pix)/6)

\int sin (\frac{π x}{6}) d x

- \frac{6}{π} cos (\frac{π x}{6}) + C

Solution steps

\int sin (\frac{π x}{6}) d x

Apply u-substitution

: \int sin (u) \frac{6}{π} d u

= \int sin (u) \frac{6}{π} d u

Take the constant out:

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

= \frac{6}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{6}{π} (- cos (u))

Substitute back

u = \frac{π x}{6}

= \frac{6}{π} (- cos (\frac{π x}{6}))

Simplify

= - \frac{6}{π} cos (\frac{π x}{6})

Add a constant to the solution

= - \frac{6}{π} cos (\frac{π x}{6}) + C

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What is the integral of sin((pix)/6) ?
The integral of sin((pix)/6) is -6/pi cos((pix)/6)+C