What is the integral from-1 to 0 of x/(e^x) ?

The integral from-1 to 0 of x/(e^x) is -1

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integral from-1 to 0 of x/(e^x)

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

- 1

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{1}{e ^{x}} d x = \frac{1}{e ^{x}}

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

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

Compute the boundaries:

- 1

= - 1

\int_{0}^{1} \frac{1}{2} (x^{2} - x^{4}) d x

\int_{- \infty}^{\infty} 2 d x

\int_{1}^{4} \frac{1}{x} - (2 x - 1) d x

\int_{3}^{0} 5 x - x^{3} d x

\int_{3}^{7} \frac{x}{x - 7} d x

What is the integral from-1 to 0 of x/(e^x) ?
The integral from-1 to 0 of x/(e^x) is -1