What is the integral from-1 to 0 of x^2e^{-2x} ?

The integral from-1 to 0 of x^2e^{-2x} is (-1+e^2)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-1 to 0 of x^2e^{-2x}

\int_{- 1}^{0} x^{2} e^{- 2 x} d x

\frac{- 1 + e ^{2}}{4}

Decimal

1.59726 \dots

Solution steps

\int_{- 1}^{0} x^{2} e^{- 2 x} d x

Apply Integration By Parts

= [- \frac{1}{2} e^{- 2 x} x^{2} - \int - e^{- 2 x} x d x]_{- 1}^{0}

\int - e^{- 2 x} x d x = - \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x})

= [- \frac{1}{2} e^{- 2 x} x^{2} - (- \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}))]_{- 1}^{0}

Simplify

= [- \frac{1}{2} e^{- 2 x} x^{2} + \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x})]_{- 1}^{0}

Compute the boundaries:

- \frac{1}{4} + \frac{e ^{2}}{4}

= - \frac{1}{4} + \frac{e ^{2}}{4}

Simplify

= \frac{- 1 + e ^{2}}{4}

What is the integral from-1 to 0 of x^2e^{-2x} ?
The integral from-1 to 0 of x^2e^{-2x} is (-1+e^2)/4