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Popular >

integral from 1 to 0 of xln(x)

Solution

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

Solution

\frac{1}{4}

+1

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} x ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- \frac{1}{4}

= - (- \frac{1}{4})

Simplify

= \frac{1}{4}

Popular Examples

integral from-1 to 1 of z

\int_{- 1}^{1} z d z

integral from 5 to 20 of x^{3/2}

\int_{5}^{20} x^{\frac{3}{2}} d x

integral from 0 to 1 of 6xy

\int_{0}^{1} 6 x y d x

integral from 0 to 5 of x/(x^2+4)

\int_{0}^{5} \frac{x}{x ^{2} + 4} d x

integral from 0 to 2pi of e^x

\int_{0}^{2 π} e^{x} d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 0 of xln(x) ?
The integral from 1 to 0 of xln(x) is 1/4