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 Notation

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