What is the integral of cos(npi x/2) ?

The integral of cos(npi x/2) is 2/(pin)sin((nxpi)/2)+C

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integral of cos(npi x/2)

\int cos (nπ \frac{x}{2}) d x

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

Solution steps

\int cos (nπ \frac{x}{2}) d x

Multiply

nπ \frac{x}{2} : \frac{πn x}{2}

= \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

\frac{d}{d x} (6 + 5 f (x))

\int_{0.1}^{0.2} 600 x d x

x \to \infty lim (x - 3)

\int \frac{1}{cos ^{2} ( θ )} d θ

y = e^{x} x^{5} + 10 e^{x} x^{4} + 20 e^{x} x^{3}

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