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

The integral of cos(pi/2 x) is 2/pi sin((pix)/2)+C

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integral of cos(pi/2 x)

\int cos (\frac{π}{2} x) d x

\frac{2}{π} sin (\frac{π x}{2}) + C

Solution steps

\int cos (\frac{π}{2} x) d x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \int cos (\frac{π x}{2}) d x

Apply u-substitution

: \int cos (u) \frac{2}{π} d u

= \int cos (u) \frac{2}{π} d u

Take the constant out:

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

= \frac{2}{π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{2}{π} sin (u)

Substitute back

u = \frac{π x}{2}

= \frac{2}{π} sin (\frac{π x}{2})

Add a constant to the solution

= \frac{2}{π} sin (\frac{π x}{2}) + C

\frac{d}{d x} ((4 x^{2} - x) (x^{3} - 8 x^{2} + 12))

f (x) = x^{2} + 3

x \to 1 lim (4 x - \frac{4}{x - 1})

\int x^{p} ln (x) d x

f (x) = (x^{2} + 9)^{\frac{1}{2}}

What is the integral of cos(pi/2 x) ?
The integral of cos(pi/2 x) is 2/pi sin((pix)/2)+C