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

The integral from 1 to 9 of (sqrt(x)-x) is -68/3

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integral from 1 to 9 of (sqrt(x)-x)

\int_{1}^{9} (x - x) d x

- \frac{68}{3}

Decimal

- 22.66666 \dots

Solution steps

\int_{1}^{9} 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_{1}^{9} x d x - \int_{1}^{9} x d x

\int_{1}^{9} x d x = \frac{52}{3}

\int_{1}^{9} x d x = 40

= \frac{52}{3} - 40

Simplify

\frac{52}{3} - 40 : - \frac{68}{3}

= - \frac{68}{3}

What is the integral from 1 to 9 of (sqrt(x)-x) ?
The integral from 1 to 9 of (sqrt(x)-x) is -68/3