What is the integral from 0 to 7 of 10xln(x) ?

The integral from 0 to 7 of 10xln(x) is 10(49/2 ln(7)-49/4)

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integral from 0 to 7 of 10xln(x)

\int_{0}^{7} 10 x ln (x) d x

10 (\frac{49}{2} ln (7) - \frac{49}{4})

Decimal

354.24798 \dots

Solution steps

\int_{0}^{7} 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}^{7} x ln (x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{7}

= 10 [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{7}

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

= 10 [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{0}^{7}

Compute the boundaries:

\frac{49}{2} ln (7) - \frac{49}{4}

= 10 (\frac{49}{2} ln (7) - \frac{49}{4})

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What is the integral from 0 to 7 of 10xln(x) ?
The integral from 0 to 7 of 10xln(x) is 10(49/2 ln(7)-49/4)