What is the integral from 0 to 0.6 of 2xe^{-x} ?

The integral from 0 to 0.6 of 2xe^{-x} is 0.24380…

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integral from 0 to 0.6 of 2xe^{-x}

\int_{0}^{0.6} 2 x e^{- x} d x

0.24380 \dots

Solution steps

\int_{0}^{0.6} 2 x e^{- x} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{0.6} x e^{- x} d x

Apply Integration By Parts

: [- e^{- x} x - \int - e^{- x} d x]_{0}^{0.6}

= 2 [- e^{- x} x - \int - e^{- x} d x]_{0}^{0.6}

\int - e^{- x} d x = e^{- x}

= 2 [- e^{- x} x - e^{- x}]_{0}^{0.6}

Compute the boundaries:

0.12190 \dots

= 2 \cdot 0.12190 \dots

Simplify

= 0.24380 \dots

y^{^{'}} = 2 y

\frac{d y}{d x} = y^{\frac{1}{3}}

x^{2} + 11, at x = 5

t^{13 t}

\frac{d}{d x} (sec (5 x) + 1)

What is the integral from 0 to 0.6 of 2xe^{-x} ?
The integral from 0 to 0.6 of 2xe^{-x} is 0.24380…