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

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

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

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

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

Decimal

- 0.80685 \dots

Solution steps

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

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

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

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

Simplify

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

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