What is the integral of sin(xpi) ?

The integral of sin(xpi) is -1/pi cos(pix)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(xpi)

\int sin (x π) d x

- \frac{1}{π} cos (π x) + C

Solution steps

\int sin (x π) d x

Apply u-substitution

: \int sin (u) \frac{1}{π} d u

= \int sin (u) \frac{1}{π} d u

Take the constant out:

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

= \frac{1}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{π} (- cos (u))

Substitute back

u = x π

= \frac{1}{π} (- cos (x π))

Simplify

= - \frac{1}{π} cos (π x)

Add a constant to the solution

= - \frac{1}{π} cos (π x) + C

\int (x lo g_{10} (2 x)) d x

(0, - 2), (6, 0)

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