What is the integral from 2 to 5 of x^3-3x^2+x ?

The integral from 2 to 5 of x^3-3x^2+x is 183/4

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integral from 2 to 5 of x^3-3x^2+x

\int_{2}^{5} x^{3} - 3 x^{2} + x d x

\frac{183}{4}

Decimal

45.75

Solution steps

\int_{2}^{5} x^{3} - 3 x^{2} + 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_{2}^{5} x^{3} d x - \int_{2}^{5} 3 x^{2} d x + \int_{2}^{5} x d x

\int_{2}^{5} x^{3} d x = \frac{609}{4}

\int_{2}^{5} 3 x^{2} d x = 117

\int_{2}^{5} x d x = \frac{21}{2}

= \frac{609}{4} - 117 + \frac{21}{2}

Simplify

\frac{609}{4} - 117 + \frac{21}{2} : \frac{183}{4}

= \frac{183}{4}

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What is the integral from 2 to 5 of x^3-3x^2+x ?
The integral from 2 to 5 of x^3-3x^2+x is 183/4