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

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

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

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

3

Solution steps

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

Expand

\frac{x - x}{x} : 1 - \frac{1}{x}

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

\int_{4}^{9} 1 d x = 5

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

= 5 - 2

Simplify

= 3

\int e^{2 x - 2} d x

\frac{d}{d x} (\frac{1}{2 x ^{2} - 3})

\int \frac{( e ^{x^{2}} - 1 )}{x} d x

\int_{0}^{1} \frac{1}{( x - 1 ) ^{2}} d x

\frac{1 + x}{1 - x}

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