What is the integral from 4 to 9 of 1/2 x-sqrt(x) ?

The integral from 4 to 9 of 1/2 x-sqrt(x) is 43/12

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integral from 4 to 9 of 1/2 x-sqrt(x)

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

\frac{43}{12}

Decimal

3.58333 \dots

Solution steps

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

\int_{4}^{9} \frac{1}{2} x d x = \frac{65}{4}

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

= \frac{65}{4} - \frac{38}{3}

Simplify

\frac{65}{4} - \frac{38}{3} : \frac{43}{12}

= \frac{43}{12}

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What is the integral from 4 to 9 of 1/2 x-sqrt(x) ?
The integral from 4 to 9 of 1/2 x-sqrt(x) is 43/12