What is the integral of cos((npit)/2) ?

The integral of cos((npit)/2) is 2/(pin)sin((ntpi)/2)+C

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integral of cos((npit)/2)

\int cos (\frac{nπ t}{2}) d t

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

Solution steps

\int cos (\frac{nπ t}{2}) 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 = \frac{n t π}{2}

= \frac{2}{πn} sin (\frac{n t π}{2})

Add a constant to the solution

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

\frac{d}{d x} (\frac{ln ( x ^{2} )}{e ^{2 x}})

\int (3 x^{2} - 4 x) e^{2 x} d x

n = 0 \sum \infty \frac{1}{n ^{2} + 3 n + 2}

x \to 0 lim (\frac{e ^{x} + e ^{- x}}{e ^{x} - e ^{- x}})

\frac{d}{d x} (1 - x)

What is the integral of cos((npit)/2) ?
The integral of cos((npit)/2) is 2/(pin)sin((ntpi)/2)+C