What is the integral from 0 to 10 of xe^{-0.6x} ?

The integral from 0 to 10 of xe^{-0.6x} is 2.72957…

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integral from 0 to 10 of xe^{-0.6x}

\int_{0}^{10} x e^{- 0.6 x} d x

2.72957 \dots

Solution steps

\int_{0}^{10} x e^{- 0.6 x} d x

Apply u-substitution

: \int_{0}^{- 6} \frac{5 e ^{u} u}{1.8} d u

= \int_{0}^{- 6} \frac{5 e ^{u} u}{1.8} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 6}^{0} \frac{5 e ^{u} u}{1.8} d u

Take the constant out:

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

= - \frac{5}{1.8} \cdot \int_{- 6}^{0} e^{u} u d u

Simplify

= - 2.77777 \dots \cdot \int_{- 6}^{0} e^{u} u d u

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{- 6}^{0}

= - 2.77777 \dots [e^{u} u - \int e^{u} d u]_{- 6}^{0}

\int e^{u} d u = e^{u}

= - 2.77777 \dots [e^{u} u - e^{u}]_{- 6}^{0}

Compute the boundaries:

- 1 + \frac{7}{e ^{6}}

= - 2.77777 \dots (- 1 + \frac{7}{e ^{6}})

Simplify

= 2.72957 \dots

\frac{\partial}{\partial y} (y (2 - x - y))

\int x (x^{2} + 1) d x

x y^{^{'}} - y^{^{'}} - (x - 1) sin (x) + y = 0

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

y = \frac{7}{3 - 4 x ^{4}}

What is the integral from 0 to 10 of xe^{-0.6x} ?
The integral from 0 to 10 of xe^{-0.6x} is 2.72957…