What is the integral from-2 to 2 of x^2e^x ?

The integral from-2 to 2 of x^2e^x is 2e^2-(10)/(e^2)

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integral from-2 to 2 of x^2e^x

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

2 e^{2} - \frac{10}{e ^{2}}

Decimal Notation

13.42475 \dots

Solution steps

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

Apply Integration By Parts

: [x^{2} e^{x} - \int 2 x e^{x} d x]_{- 2}^{2}

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

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

= [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{- 2}^{2}

Compute the boundaries:

2 e^{2} - \frac{10}{e ^{2}}

= 2 e^{2} - \frac{10}{e ^{2}}

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What is the integral from-2 to 2 of x^2e^x ?
The integral from-2 to 2 of x^2e^x is 2e^2-(10)/(e^2)