What is the integral from 1 to 9 of y(3-sqrt(y)) ?

The integral from 1 to 9 of y(3-sqrt(y)) is 116/5

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integral from 1 to 9 of y(3-sqrt(y))

\int_{1}^{9} y (3 - y) d y

\frac{116}{5}

Decimal

23.2

Solution steps

\int_{1}^{9} y (3 - y) d y

Expand

y (3 - y) : 3 y - y^{\frac{3}{2}}

= \int_{1}^{9} 3 y - y^{\frac{3}{2}} d y

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} 3 y d y - \int_{1}^{9} y^{\frac{3}{2}} d y

\int_{1}^{9} 3 y d y = 120

\int_{1}^{9} y^{\frac{3}{2}} d y = \frac{484}{5}

= 120 - \frac{484}{5}

Simplify

120 - \frac{484}{5} : \frac{116}{5}

= \frac{116}{5}

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What is the integral from 1 to 9 of y(3-sqrt(y)) ?
The integral from 1 to 9 of y(3-sqrt(y)) is 116/5