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

The integral from-2 to 4 of |x^3-4x^2+3x| is 86/3

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

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

\frac{86}{3}

Decimal

28.66666 \dots

Solution steps

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

Eliminate Absolutes

= \int_{- 2}^{0} - x^{3} + 4 x^{2} - 3 x d x + \int_{0}^{1} x^{3} - 4 x^{2} + 3 x d x + \int_{1}^{3} - x^{3} + 4 x^{2} - 3 x d x + \int_{3}^{4} x^{3} - 4 x^{2} + 3 x d x

\int_{- 2}^{0} - x^{3} + 4 x^{2} - 3 x d x = \frac{62}{3}

\int_{0}^{1} x^{3} - 4 x^{2} + 3 x d x = \frac{5}{12}

\int_{1}^{3} - x^{3} + 4 x^{2} - 3 x d x = \frac{8}{3}

\int_{3}^{4} x^{3} - 4 x^{2} + 3 x d x = \frac{59}{12}

= \frac{62}{3} + \frac{5}{12} + \frac{8}{3} + \frac{59}{12}

Simplify

\frac{62}{3} + \frac{5}{12} + \frac{8}{3} + \frac{59}{12} : \frac{86}{3}

= \frac{86}{3}

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What is the integral from-2 to 4 of |x^3-4x^2+3x| ?
The integral from-2 to 4 of |x^3-4x^2+3x| is 86/3