What is the integral from 0 to 2 of x^2e^x ?

The integral from 0 to 2 of x^2e^x is 2e^2-2

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integral from 0 to 2 of x^2e^x

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

2 e^{2} - 2

Decimal

12.77811 \dots

Solution steps

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

Apply Integration By Parts

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

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

= [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{0}^{2}

Compute the boundaries:

2 e^{2} - 2

= 2 e^{2} - 2

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