What is the integral from 0 to y of e^{-y} ?

The integral from 0 to y of e^{-y} is -e^{-y}+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to y of e^{-y}

\int_{0}^{y} e^{- y} d y

- e^{- y} + 1

Solution steps

\int_{0}^{y} e^{- y} d y

Apply u-substitution

: \int_{0}^{- y} - e^{u} d u

= \int_{0}^{- y} - e^{u} d u

Take the constant out:

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

= - \int_{0}^{- y} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - [e^{u}]_{0}^{- y}

Compute the boundaries:

e^{- y} - 1

= - (e^{- y} - 1)

Simplify

= - e^{- y} + 1

\int_{1}^{3} 5 x^{2} d x

\int_{0}^{1} x (x + 1)^{- 3} d x

\int_{0}^{1} 1 + u^{2} d u

\int_{0}^{π} 2 sin (x) - sin (2 x) d x

\int_{2}^{1} x d x

What is the integral from 0 to y of e^{-y} ?
The integral from 0 to y of e^{-y} is -e^{-y}+1