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

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

Popular >

integral of cos((npix)/2)

\int cos (\frac{nπ x}{2}) d x

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

Solution steps

\int cos (\frac{nπ 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

x \to 3 + lim (\frac{3}{x - 3} - 2 x)

\frac{d}{d x} (ln (3 x + 5 y))

\frac{d}{d x} (\frac{1}{4 x - 7})

x \to 0 + lim ((1 + tan (x))^{\frac{3}{x}})

\frac{\partial}{\partial x} (56 y^{6} x^{6} - 42 y^{5} x^{5})

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