What is the integral from 2 to 3 of x^3-5x^2+6x ?

The integral from 2 to 3 of x^3-5x^2+6x is -5/12

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integral from 2 to 3 of x^3-5x^2+6x

\int_{2}^{3} x^{3} - 5 x^{2} + 6 x d x

- \frac{5}{12}

Decimal

- 0.41666 \dots

Solution steps

\int_{2}^{3} x^{3} - 5 x^{2} + 6 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}^{3} x^{3} d x - \int_{2}^{3} 5 x^{2} d x + \int_{2}^{3} 6 x d x

\int_{2}^{3} x^{3} d x = \frac{65}{4}

\int_{2}^{3} 5 x^{2} d x = \frac{95}{3}

\int_{2}^{3} 6 x d x = 15

= \frac{65}{4} - \frac{95}{3} + 15

Simplify

\frac{65}{4} - \frac{95}{3} + 15 : - \frac{5}{12}

= - \frac{5}{12}

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What is the integral from 2 to 3 of x^3-5x^2+6x ?
The integral from 2 to 3 of x^3-5x^2+6x is -5/12