What is the integral from 0 to 8 of t^3-10t^2+24t ?

The integral from 0 to 8 of t^3-10t^2+24t is 256/3

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integral from 0 to 8 of t^3-10t^2+24t

\int_{0}^{8} t^{3} - 10 t^{2} + 24 t d t

\frac{256}{3}

Decimal

85.33333 \dots

Solution steps

\int_{0}^{8} t^{3} - 10 t^{2} + 24 t 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}^{8} t^{3} d t - \int_{0}^{8} 10 t^{2} d t + \int_{0}^{8} 24 t d t

\int_{0}^{8} t^{3} d t = 1024

\int_{0}^{8} 10 t^{2} d t = \frac{5120}{3}

\int_{0}^{8} 24 t d t = 768

= 1024 - \frac{5120}{3} + 768

Simplify

1024 - \frac{5120}{3} + 768 : \frac{256}{3}

= \frac{256}{3}

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What is the integral from 0 to 8 of t^3-10t^2+24t ?
The integral from 0 to 8 of t^3-10t^2+24t is 256/3