What is the integral of 1cos((npix)/2) ?

The integral of 1cos((npix)/2) is 2/(pin)sin((nxpi)/2)+C

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integral of 1cos((npix)/2)

\int 1 cos (\frac{nπ x}{2}) d x

\frac{2}{πn} sin (\frac{n x π}{2}) + C

Solution steps

\int 1 \cdot cos (\frac{nπ x}{2}) d x

Simplify

= \int cos (\frac{πn x}{2}) d x

Apply u-substitution

: \int \frac{2 cos ( u )}{πn} d u

= \int \frac{2 cos ( u )}{πn} d u

Take the constant out:

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

= \frac{2}{πn} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{2}{πn} sin (u)

Substitute back

u = \frac{n x π}{2}

= \frac{2}{πn} sin (\frac{n x π}{2})

Add a constant to the solution

= \frac{2}{πn} sin (\frac{n x π}{2}) + C

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What is the integral of 1cos((npix)/2) ?
The integral of 1cos((npix)/2) is 2/(pin)sin((nxpi)/2)+C