What is the integral from 0 to 9 of 3sqrt(x)-x ?

The integral from 0 to 9 of 3sqrt(x)-x is 27/2

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integral from 0 to 9 of 3sqrt(x)-x

\int_{0}^{9} 3 x - x d x

\frac{27}{2}

Solution steps

\int_{0}^{9} 3 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_{0}^{9} 3 x d x - \int_{0}^{9} x d x

\int_{0}^{9} 3 x d x = 54

\int_{0}^{9} x d x = \frac{81}{2}

= 54 - \frac{81}{2}

Simplify

54 - \frac{81}{2} : \frac{27}{2}

= \frac{27}{2}

\int \frac{x}{( x - 1 ) ^{2} + 1} d x

\int x e^{3} d x

- \frac{48 x}{( x ^{2} + 12 ) ^{2}}

\int_{0}^{9} \frac{1}{x ^{2} - 6 x + 5} d x

\frac{1}{1 + x ^{2}}, \frac{x ^{2}}{2}

What is the integral from 0 to 9 of 3sqrt(x)-x ?
The integral from 0 to 9 of 3sqrt(x)-x is 27/2