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

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

Popular >

integral of sin((pix)/y)

\int sin (\frac{π x}{y}) d x

- \frac{y}{π} cos (\frac{π x}{y}) + C

Solution steps

\int sin (\frac{π x}{y}) d x

Apply u-substitution

: \int \frac{y sin ( u )}{π} d u

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

Use the common integral:

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

= \frac{y}{π} (- cos (u))

Substitute back

u = \frac{x π}{y}

= \frac{y}{π} (- cos (\frac{x π}{y}))

Simplify

= - \frac{y}{π} cos (\frac{π x}{y})

Add a constant to the solution

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

\int \frac{1}{x ^{2} ( x ^{2} + 4 ) ^{2}} d x

\int 7 t e^{6 t} d t

\int \frac{- 3}{x} d x

\int 2 π cos (π) x d x

\int \frac{1}{1 + sec ( a x )} d x

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