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 -5/e+2

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integral from 0 to 1 of (x^2)/(e^x)

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

- \frac{5}{e} + 2

Decimal Notation

0.16060 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{2 x}{e ^{x}} d x = - 2 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}})

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

Simplify

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

Compute the boundaries:

- \frac{5}{e} + 2

= - \frac{5}{e} + 2

x \to 2 lim (\frac{5}{( x - 5 ) ^{2}})

3 y^{^{''}} - 6 y^{^{'}} + 6 y = 0

- x^{2} - 2 x + 9, [- 4, 0]

f (x) = arcsin (8 t)

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 -5/e+2