What is the integral from 1 to 2 of 1/x-x/4 ?

The integral from 1 to 2 of 1/x-x/4 is ln(2)-3/8

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integral from 1 to 2 of 1/x-x/4

\int_{1}^{2} \frac{1}{x} - \frac{x}{4} d x

ln (2) - \frac{3}{8}

Decimal

0.31814 \dots

Solution steps

\int_{1}^{2} \frac{1}{x} - \frac{x}{4} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} \frac{1}{x} d x - \int_{1}^{2} \frac{x}{4} d x

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

\int_{1}^{2} \frac{x}{4} d x = \frac{3}{8}

= ln (2) - \frac{3}{8}

What is the integral from 1 to 2 of 1/x-x/4 ?
The integral from 1 to 2 of 1/x-x/4 is ln(2)-3/8