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

The integral from 0 to 1 of x^2*e^x is e-2

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

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

e - 2

Decimal

0.71828 \dots

Solution steps

\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}

= [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})

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

Compute the boundaries:

e - 2

= e - 2

\int_{0}^{\frac{π}{2}} - cos (x) d x

\int_{0}^{4} (x^{3} - x^{2} + 1) d x

\int_{- 5}^{4} - x^{2} - 3 x d x

\int_{1}^{2} (3 x^{2} - 2 x + 1) d x

\int_{0}^{1} x cos (πn x) d x

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