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Popular Calculus >

integral from 1 to 2 of x-1/x

Solution

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

Solution

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

+1

Decimal

0.80685 \dots

Solution steps

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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