What is the integral from-3 to 0 of xe^x ?

The integral from-3 to 0 of xe^x is -1+4/(e^3)

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integral from-3 to 0 of xe^x

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

- 1 + \frac{4}{e ^{3}}

Decimal Notation

- 0.80085 \dots

Solution steps

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

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{- 3}^{0}

= [e^{x} x - \int e^{x} d x]_{- 3}^{0}

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

= [e^{x} x - e^{x}]_{- 3}^{0}

Compute the boundaries:

- 1 + \frac{4}{e ^{3}}

= - 1 + \frac{4}{e ^{3}}

\int_{0}^{2} (3 x)^{2} d x

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

\int_{0}^{2} 2 x^{3} - 2 d x

\int_{- 1}^{4} \frac{1}{∣ x ∣} d x

\int_{0}^{1} (1 - x^{2})^{\frac{5}{2}} d x

What is the integral from-3 to 0 of xe^x ?
The integral from-3 to 0 of xe^x is -1+4/(e^3)