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

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

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

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

\frac{256}{3}

Decimal

85.33333 \dots

Solution steps

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

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

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

\int_{0}^{8} 24 x d x = 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 x^3-10x^2+24x ?
The integral from 0 to 8 of x^3-10x^2+24x is 256/3