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

The integral from 0 to 4 of (4t^2+t^{3/2}) is 1472/15

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

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

\frac{1472}{15}

Decimal

98.13333 \dots

Solution steps

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

\int_{0}^{4} 4 t^{2} d t = \frac{256}{3}

\int_{0}^{4} t^{\frac{3}{2}} d t = \frac{64}{5}

= \frac{256}{3} + \frac{64}{5}

Simplify

\frac{256}{3} + \frac{64}{5} : \frac{1472}{15}

= \frac{1472}{15}

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What is the integral from 0 to 4 of (4t^2+t^{3/2}) ?
The integral from 0 to 4 of (4t^2+t^{3/2}) is 1472/15