What is the integral from 0 to 1 of 3x^2e^x ?

The integral from 0 to 1 of 3x^2e^x is 3(e-2)

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integral from 0 to 1 of 3x^2e^x

\int_{0}^{1} 3 x^{2} e^{x} d x

3 (e - 2)

Decimal Notation

2.15484 \dots

Solution steps

\int_{0}^{1} 3 x^{2} e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{0}^{1} x^{2} e^{x} d x

Apply Integration By Parts

: [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{1}

= 3 [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{1}

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

= 3 [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{0}^{1}

Compute the boundaries:

e - 2

= 3 (e - 2)

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What is the integral from 0 to 1 of 3x^2e^x ?
The integral from 0 to 1 of 3x^2e^x is 3(e-2)