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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sin((pix)/(2y))

\int sin (\frac{π x}{2 y}) d x

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

Solution steps

\int sin (\frac{π x}{2 y}) d x

Apply u-substitution

= \int \frac{2 y sin ( u )}{π} d u

Take the constant out:

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

= \frac{2 y}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{2 y}{π} (- cos (u))

Substitute back

u = \frac{x π}{2 y}

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

Simplify

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

Add a constant to the solution

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

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