What is the integral from 4 to 16 of x/2-sqrt(x) ?

The integral from 4 to 16 of x/2-sqrt(x) is 68/3

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integral from 4 to 16 of x/2-sqrt(x)

\int_{4}^{16} \frac{x}{2} - x d x

\frac{68}{3}

Decimal

22.66666 \dots

Solution steps

\int_{4}^{16} \frac{x}{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_{4}^{16} \frac{x}{2} d x - \int_{4}^{16} x d x

\int_{4}^{16} \frac{x}{2} d x = 60

\int_{4}^{16} x d x = \frac{112}{3}

= 60 - \frac{112}{3}

Simplify

60 - \frac{112}{3} : \frac{68}{3}

= \frac{68}{3}

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What is the integral from 4 to 16 of x/2-sqrt(x) ?
The integral from 4 to 16 of x/2-sqrt(x) is 68/3