What is the integral from 0 to 0.1 of xe^{0.1x} ?

The integral from 0 to 0.1 of xe^{0.1x} is 0.00503…

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integral from 0 to 0.1 of xe^{0.1x}

\int_{0}^{0.1} x e^{0.1 x} d x

0.00503 \dots

Solution steps

\int_{0}^{0.1} x e^{0.1 x} d x

Apply Integration By Parts

: [10 e^{0.1 x} x - \int 10 e^{0.1 x} d x]_{0}^{0.1}

= [10 e^{0.1 x} x - \int 10 e^{0.1 x} d x]_{0}^{0.1}

\int 10 e^{0.1 x} d x = 100 e^{0.1 x}

= [10 e^{0.1 x} x - 100 e^{0.1 x}]_{0}^{0.1}

Compute the boundaries:

0.00503 \dots

= 0.00503 \dots

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What is the integral from 0 to 0.1 of xe^{0.1x} ?
The integral from 0 to 0.1 of xe^{0.1x} is 0.00503…