What is the integral from 4 to 9 of (sqrt(x)+1/(3sqrt(x))) ?

The integral from 4 to 9 of (sqrt(x)+1/(3sqrt(x))) is 40/3

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integral from 4 to 9 of (sqrt(x)+1/(3sqrt(x)))

\int_{4}^{9} (x + \frac{1}{3 x}) d x

\frac{40}{3}

Decimal

13.33333 \dots

Solution steps

\int_{4}^{9} x + \frac{1}{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{1}{3 x} d x

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

\int_{4}^{9} \frac{1}{3 x} d x = \frac{2}{3}

= \frac{38}{3} + \frac{2}{3}

Simplify

\frac{38}{3} + \frac{2}{3} : \frac{40}{3}

= \frac{40}{3}

What is the integral from 4 to 9 of (sqrt(x)+1/(3sqrt(x))) ?
The integral from 4 to 9 of (sqrt(x)+1/(3sqrt(x))) is 40/3