What is the integral from 1 to 4 of (3x-2)/(sqrt(x)) ?

The integral from 1 to 4 of (3x-2)/(sqrt(x)) is 10

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integral from 1 to 4 of (3x-2)/(sqrt(x))

\int_{1}^{4} \frac{3 x - 2}{x} d x

10

Solution steps

\int_{1}^{4} \frac{3 x - 2}{x} d x

Expand

\frac{3 x - 2}{x} : 3 x - \frac{2}{x}

= \int_{1}^{4} 3 x - \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_{1}^{4} 3 x d x - \int_{1}^{4} \frac{2}{x} d x

\int_{1}^{4} 3 x d x = 14

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

= 14 - 4

Simplify

= 10

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What is the integral from 1 to 4 of (3x-2)/(sqrt(x)) ?
The integral from 1 to 4 of (3x-2)/(sqrt(x)) is 10