What is the integral of sin(pit) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(pit)

\int sin (π t) d t

- \frac{1}{π} cos (π t) + C

Solution steps

\int sin (π t) d t

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 = π t

= \frac{1}{π} (- cos (π t))

Simplify

= - \frac{1}{π} cos (π t)

Add a constant to the solution

= - \frac{1}{π} cos (π t) + C

\frac{d y}{d x} = \frac{x - 3}{y - 4}

\frac{\partial}{\partial x} ((2 x^{3} - 4 y) (2 x^{2} - 4))

\frac{d}{d x} (cos (\frac{π}{2}))

\int \frac{1}{x ^{2} - 2 x + 8} d x

\int \frac{1}{3 x} d x