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

Lösung

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

185.24451 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [- 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}

Vereinfache

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

Berechne die Grenzen:

185.24451 \dots

= 185.24451 \dots

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

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

d er i v a t i v e \frac{( x ^{\frac{1}{3}} - 4 )}{x ^{\frac{7}{2}}}

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

d er i v a t i v e y = \frac{csc ( x ^{2} )}{7 x - cos ^{2} ( x )}