What is the integral from 4 to 10 of x/4-4/x ?

The integral from 4 to 10 of x/4-4/x is 21/2-4ln(5/2)

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integral from 4 to 10 of x/4-4/x

\int_{4}^{10} \frac{x}{4} - \frac{4}{x} d x

\frac{21}{2} - 4 ln (\frac{5}{2})

Decimal

6.83483 \dots

Solution steps

\int_{4}^{10} \frac{x}{4} - \frac{4}{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}^{10} \frac{x}{4} d x - \int_{4}^{10} \frac{4}{x} d x

\int_{4}^{10} \frac{x}{4} d x = \frac{21}{2}

\int_{4}^{10} \frac{4}{x} d x = 4 ln (\frac{5}{2})

= \frac{21}{2} - 4 ln (\frac{5}{2})

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What is the integral from 4 to 10 of x/4-4/x ?
The integral from 4 to 10 of x/4-4/x is 21/2-4ln(5/2)