What is the integral from 2 to 10 of x/2-2/x ?

The integral from 2 to 10 of x/2-2/x is 24-2ln(5)

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integral from 2 to 10 of x/2-2/x

\int_{2}^{10} \frac{x}{2} - \frac{2}{x} d x

24 - 2 ln (5)

Decimal

20.78112 \dots

Solution steps

\int_{2}^{10} \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_{2}^{10} \frac{x}{2} d x - \int_{2}^{10} \frac{2}{x} d x

\int_{2}^{10} \frac{x}{2} d x = 24

\int_{2}^{10} \frac{2}{x} d x = 2 ln (5)

= 24 - 2 ln (5)

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

\int_{0}^{2 π} (sin^{2} (t)) d t

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

\int_{- \frac{π}{2}}^{\frac{π}{2}} 3 cos^{3} (x) d x

\int_{0}^{1} \frac{10}{t ^{2} + 1} d t

What is the integral from 2 to 10 of x/2-2/x ?
The integral from 2 to 10 of x/2-2/x is 24-2ln(5)