What is the integral from 0 to 9 of 4t^2+t^{3/2} ?

The integral from 0 to 9 of 4t^2+t^{3/2} is 5346/5

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integral from 0 to 9 of 4t^2+t^{3/2}

\int_{0}^{9} 4 t^{2} + t^{\frac{3}{2}} d t

\frac{5346}{5}

Decimal

1069.2

Solution steps

\int_{0}^{9} 4 t^{2} + t^{\frac{3}{2}} d t

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} 4 t^{2} d t + \int_{0}^{9} t^{\frac{3}{2}} d t

\int_{0}^{9} 4 t^{2} d t = 972

\int_{0}^{9} t^{\frac{3}{2}} d t = \frac{486}{5}

= 972 + \frac{486}{5}

Simplify

972 + \frac{486}{5} : \frac{5346}{5}

= \frac{5346}{5}

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What is the integral from 0 to 9 of 4t^2+t^{3/2} ?
The integral from 0 to 9 of 4t^2+t^{3/2} is 5346/5