What is the integral from 0 to 3 of x(1.33x^2-3) ?

The integral from 0 to 3 of x(1.33x^2-3) is 13.4325

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integral from 0 to 3 of x(1.33x^2-3)

\int_{0}^{3} x (1.33 x^{2} - 3) d x

13.4325

Solution steps

\int_{0}^{3} x (1.33 x^{2} - 3) d x

Expand

x (1.33 x^{2} - 3) : 1.33 x^{3} - 3 x

= \int_{0}^{3} 1.33 x^{3} - 3 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}^{3} 1.33 x^{3} d x - \int_{0}^{3} 3 x d x

\int_{0}^{3} 1.33 x^{3} d x = 26.9325

\int_{0}^{3} 3 x d x = \frac{27}{2}

= 26.9325 - \frac{27}{2}

Simplify

= 13.4325

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What is the integral from 0 to 3 of x(1.33x^2-3) ?
The integral from 0 to 3 of x(1.33x^2-3) is 13.4325