What is the integral from 0 to 1/10 of xln(10x) ?

The integral from 0 to 1/10 of xln(10x) is -1/400

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integral from 0 to 1/10 of xln(10x)

\int_{0}^{\frac{1}{10}} x ln (10 x) d x

- \frac{1}{400}

Decimal Notation

- 0.0025

Solution steps

\int_{0}^{\frac{1}{10}} x ln (10 x) d x

Apply Integration By Parts

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

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

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

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

2 \cdot \frac{x ^{2}}{4} = \frac{x ^{2}}{2}

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

Compute the boundaries:

- \frac{1}{400}

= - \frac{1}{400}

x \to 0 lim (2)

f (x) = 3 tan (x), at x = \frac{π}{3}

\int_{- \infty}^{0} x d x

\frac{1}{2} \cdot \frac{d y}{d x} = \frac{2 x}{3 y}

\frac{d ^{2}}{d x ^{2}} (3 e^{x^{2}})

What is the integral from 0 to 1/10 of xln(10x) ?
The integral from 0 to 1/10 of xln(10x) is -1/400