What is the integral from 0 to 2 of 10x*ln(x) ?

The integral from 0 to 2 of 10x*ln(x) is 10(2ln(2)-1)

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integral from 0 to 2 of 10x*ln(x)

\int_{0}^{2} 10 x \cdot ln (x) d x

10 (2 ln (2) - 1)

Decimal Notation

3.86294 \dots

Solution steps

\int_{0}^{2} 10 x ln (x) d x

Take the constant out:

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

= 10 \cdot \int_{0}^{2} x ln (x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{2}

= 10 [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{2}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 10 [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{0}^{2}

Compute the boundaries:

2 ln (2) - 1

= 10 (2 ln (2) - 1)

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What is the integral from 0 to 2 of 10x*ln(x) ?
The integral from 0 to 2 of 10x*ln(x) is 10(2ln(2)-1)