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Popular Calculus >

integral from 0 to 1 of xe^x-e^x

Solution

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

Solution

- e + 2

+1

Decimal

- 0.71828 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{1} x e^{x} d x = 1

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

= 1 - (e - 1)

Simplify

= - e + 2

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of xe^x-e^x ?
The integral from 0 to 1 of xe^x-e^x is -e+2