What is the integral of pi/(200)sin((pix)/(100)) ?

The integral of pi/(200)sin((pix)/(100)) is -1/2 cos((pix)/(100))+C

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integral of pi/(200)sin((pix)/(100))

\int \frac{π}{200} sin (\frac{π x}{100}) d x

- \frac{1}{2} cos (\frac{π x}{100}) + C

Solution steps

\int \frac{π}{200} sin (\frac{π x}{100}) d x

Take the constant out:

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

= \frac{π}{200} \cdot \int sin (\frac{π x}{100}) d x

Apply u-substitution

= \frac{π}{200} \cdot \int sin (u) \frac{100}{π} d u

Take the constant out:

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

= \frac{π}{200} \cdot \frac{100}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{π}{200} \cdot \frac{100}{π} (- cos (u))

Substitute back

u = \frac{π x}{100}

= \frac{π}{200} \cdot \frac{100}{π} (- cos (\frac{π x}{100}))

Simplify

\frac{π}{200} \cdot \frac{100}{π} (- cos (\frac{π x}{100})) : - \frac{1}{2} cos (\frac{π x}{100})

= - \frac{1}{2} cos (\frac{π x}{100})

Add a constant to the solution

= - \frac{1}{2} cos (\frac{π x}{100}) + C

What is the integral of pi/(200)sin((pix)/(100)) ?
The integral of pi/(200)sin((pix)/(100)) is -1/2 cos((pix)/(100))+C