What is the integral from 0 to 10 of x^2e^{-0.08x} ?

The integral from 0 to 10 of x^2e^{-0.08x} is 185.24451…

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integral from 0 to 10 of x^2e^{-0.08x}

\int_{0}^{10} x^{2} e^{- 0.08 x} d x

185.24451 \dots

Solution steps

\int_{0}^{10} x^{2} e^{- 0.08 x} d x

Apply Integration By Parts

: [- 12.5 e^{- 0.08 x} x^{2} - \int - 25 e^{- 0.08 x} x d x]_{0}^{10}

= [- 12.5 e^{- 0.08 x} x^{2} - \int - 25 e^{- 0.08 x} x d x]_{0}^{10}

\int - 25 e^{- 0.08 x} x d x = - 3906.25 (- 0.08 e^{- 0.08 x} x - e^{- 0.08 x})

= [- 12.5 e^{- 0.08 x} x^{2} - (- 3906.25 (- 0.08 e^{- 0.08 x} x - e^{- 0.08 x}))]_{0}^{10}

Simplify

= [- 12.5 e^{- 0.08 x} x^{2} + 3906.25 (- 0.08 e^{- 0.08 x} x - e^{- 0.08 x})]_{0}^{10}

Compute the boundaries:

185.24451 \dots

= 185.24451 \dots

\frac{\partial}{\partial y} (y^{5} cos (3 x))

\int - \frac{x}{2} d x

\frac{( x ^{\frac{1}{3}} - 4 )}{x ^{\frac{7}{2}}}

\frac{d y}{d t} = t^{2}

y = \frac{csc ( x ^{2} )}{7 x - cos ^{2} ( x )}

What is the integral from 0 to 10 of x^2e^{-0.08x} ?
The integral from 0 to 10 of x^2e^{-0.08x} is 185.24451…