What is the integral of sin((pix)/2) ?

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

Popular >

integral of sin((pix)/2)

\int sin (\frac{π x}{2}) d x

- \frac{2}{π} cos (\frac{π x}{2}) + C

Solution steps

\int sin (\frac{π x}{2}) d x

Apply u-substitution

: \int sin (u) \frac{2}{π} d u

= \int sin (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 sin (u) d u

Use the common integral:

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

= \frac{2}{π} (- cos (u))

Substitute back

u = \frac{π x}{2}

= \frac{2}{π} (- cos (\frac{π x}{2}))

Simplify

= - \frac{2}{π} cos (\frac{π x}{2})

Add a constant to the solution

= - \frac{2}{π} cos (\frac{π x}{2}) + C

ln (x - x^{2})

\frac{d}{d x} (\frac{4 π x + 3 x ^{6}}{x})

x \to 0 lim (\frac{7}{x} - \frac{7}{x ^{2} + x})

(2 a + 1)^{2}

\frac{s + 2}{s ^{2} + s + 1}

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