What is the integral from 1 to 3 of x^3-4x^2+3x ?

The integral from 1 to 3 of x^3-4x^2+3x is -8/3

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integral from 1 to 3 of x^3-4x^2+3x

\int_{1}^{3} x^{3} - 4 x^{2} + 3 x d x

- \frac{8}{3}

Decimal

- 2.66666 \dots

Solution steps

\int_{1}^{3} x^{3} - 4 x^{2} + 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_{1}^{3} x^{3} d x - \int_{1}^{3} 4 x^{2} d x + \int_{1}^{3} 3 x d x

\int_{1}^{3} x^{3} d x = 20

\int_{1}^{3} 4 x^{2} d x = \frac{104}{3}

\int_{1}^{3} 3 x d x = 12

= 20 - \frac{104}{3} + 12

Simplify

20 - \frac{104}{3} + 12 : - \frac{8}{3}

= - \frac{8}{3}

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What is the integral from 1 to 3 of x^3-4x^2+3x ?
The integral from 1 to 3 of x^3-4x^2+3x is -8/3