What is the integral from 4 to 9 of (x-3)/(sqrt(x)) ?

The integral from 4 to 9 of (x-3)/(sqrt(x)) is 20/3

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integral from 4 to 9 of (x-3)/(sqrt(x))

\int_{4}^{9} \frac{x - 3}{x} d x

\frac{20}{3}

Decimal Notation

6.66666 \dots

Solution steps

\int_{4}^{9} \frac{x - 3}{x} d x

Expand

\frac{x - 3}{x} : x - \frac{3}{x}

= \int_{4}^{9} x - \frac{3}{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}^{9} x d x - \int_{4}^{9} \frac{3}{x} d x

\int_{4}^{9} x d x = \frac{38}{3}

\int_{4}^{9} \frac{3}{x} d x = 6

= \frac{38}{3} - 6

Simplify

\frac{38}{3} - 6 : \frac{20}{3}

= \frac{20}{3}

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What is the integral from 4 to 9 of (x-3)/(sqrt(x)) ?
The integral from 4 to 9 of (x-3)/(sqrt(x)) is 20/3