What is the integral from 4 to 9 of (1/(sqrt(x))-2) ?

The integral from 4 to 9 of (1/(sqrt(x))-2) is -8

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integral from 4 to 9 of (1/(sqrt(x))-2)

\int_{4}^{9} (\frac{1}{x} - 2) d x

- 8

Solution steps

\int_{4}^{9} \frac{1}{x} - 2 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}^{9} \frac{1}{x} d x - \int_{4}^{9} 2 d x

\int_{4}^{9} \frac{1}{x} d x = 2

\int_{4}^{9} 2 d x = 10

= 2 - 10

Simplify

= - 8

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What is the integral from 4 to 9 of (1/(sqrt(x))-2) ?
The integral from 4 to 9 of (1/(sqrt(x))-2) is -8