What is the integral of cos(n pi/2 t) ?

The integral of cos(n pi/2 t) is 2/(pin)sin(n pi/2 t)+C

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integral of cos(n pi/2 t)

\int cos (n \frac{π}{2} t) d t

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

Solution steps

\int cos (n \frac{π}{2} t) d t

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 = n \frac{π}{2} t

= \frac{2}{πn} sin (n \frac{π}{2} t)

Add a constant to the solution

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

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What is the integral of cos(n pi/2 t) ?
The integral of cos(n pi/2 t) is 2/(pin)sin(n pi/2 t)+C