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

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

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integral from 1 to 2 of (x/2-2/x)

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

\frac{3}{4} - 2 ln (2)

Decimal Notation

- 0.63629 \dots

Solution steps

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

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

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

= \frac{3}{4} - 2 ln (2)

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