What is the integral from 4 to 5 of (2/(sqrt(x))-x) ?

The integral from 4 to 5 of (2/(sqrt(x))-x) is 4sqrt(5)-25/2

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integral from 4 to 5 of (2/(sqrt(x))-x)

\int_{4}^{5} (\frac{2}{x} - x) d x

45 - \frac{25}{2}

Decimal Notation

- 3.55572 \dots

Solution steps

\int_{4}^{5} \frac{2}{x} - 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_{4}^{5} \frac{2}{x} d x - \int_{4}^{5} x d x

\int_{4}^{5} \frac{2}{x} d x = 2 (25 - 4)

\int_{4}^{5} x d x = \frac{9}{2}

= 2 (25 - 4) - \frac{9}{2}

Simplify

2 (25 - 4) - \frac{9}{2} : 45 - \frac{25}{2}

= 45 - \frac{25}{2}

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What is the integral from 4 to 5 of (2/(sqrt(x))-x) ?
The integral from 4 to 5 of (2/(sqrt(x))-x) is 4sqrt(5)-25/2