What is the integral from 1/4 to 2 of ln(x) ?

The integral from 1/4 to 2 of ln(x) is -7/4+5/2 ln(2)

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integral from 1/4 to 2 of ln(x)

\int_{\frac{1}{4}}^{2} ln (x) d x

- \frac{7}{4} + \frac{5}{2} ln (2)

Decimal

- 0.01713 \dots

Solution steps

\int_{\frac{1}{4}}^{2} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{\frac{1}{4}}^{2}

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

\int 1 d x = x

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

Compute the boundaries:

- \frac{7}{4} + \frac{5}{2} ln (2)

= - \frac{7}{4} + \frac{5}{2} ln (2)

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What is the integral from 1/4 to 2 of ln(x) ?
The integral from 1/4 to 2 of ln(x) is -7/4+5/2 ln(2)