What is the integral of 14sin((pix)/(12)) ?

The integral of 14sin((pix)/(12)) is -(168)/pi cos((pix)/(12))+C

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integral of 14sin((pix)/(12))

\int 14 sin (\frac{π x}{12}) d x

- \frac{168}{π} cos (\frac{π x}{12}) + C

Solution steps

\int 14 sin (\frac{π x}{12}) d x

Take the constant out:

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

= 14 \cdot \int sin (\frac{π x}{12}) d x

Apply u-substitution

: \int sin (u) \frac{12}{π} d u

= 14 \cdot \int sin (u) \frac{12}{π} d u

Take the constant out:

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

= 14 \cdot \frac{12}{π} \cdot \int sin (u) d u

Use the common integral:

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

= 14 \cdot \frac{12}{π} (- cos (u))

Substitute back

u = \frac{π x}{12}

= 14 \cdot \frac{12}{π} (- cos (\frac{π x}{12}))

Simplify

14 \cdot \frac{12}{π} (- cos (\frac{π x}{12})) : - \frac{168}{π} cos (\frac{π x}{12})

= - \frac{168}{π} cos (\frac{π x}{12})

Add a constant to the solution

= - \frac{168}{π} cos (\frac{π x}{12}) + C

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What is the integral of 14sin((pix)/(12)) ?
The integral of 14sin((pix)/(12)) is -(168)/pi cos((pix)/(12))+C