What is the integral of sin((npix)/(40)) ?

The integral of sin((npix)/(40)) is -(40)/(pin)cos((pinx)/(40))+C

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integral of sin((npix)/(40))

\int sin (\frac{nπ x}{40}) d x

- \frac{40}{πn} cos (\frac{πn x}{40}) + C

Solution steps

\int sin (\frac{nπ x}{40}) d x

Apply u-substitution

: \int \frac{40 sin ( u )}{πn} d u

= \int \frac{40 sin ( u )}{πn} d u

Take the constant out:

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

= \frac{40}{πn} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{40}{πn} (- cos (u))

Substitute back

u = \frac{n x π}{40}

= \frac{40}{πn} (- cos (\frac{n x π}{40}))

Simplify

= - \frac{40}{πn} cos (\frac{πn x}{40})

Add a constant to the solution

= - \frac{40}{πn} cos (\frac{πn x}{40}) + C

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What is the integral of sin((npix)/(40)) ?
The integral of sin((npix)/(40)) is -(40)/(pin)cos((pinx)/(40))+C