What is the integral from 0 to 3 of |x^3-4x^2+3x| ?

The integral from 0 to 3 of |x^3-4x^2+3x| is 37/12

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integral from 0 to 3 of |x^3-4x^2+3x|

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

\frac{37}{12}

Decimal Notation

3.08333 \dots

Solution steps

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

Eliminate Absolutes

= \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_{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}

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

Simplify

\frac{5}{12} + \frac{8}{3} : \frac{37}{12}

= \frac{37}{12}

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What is the integral from 0 to 3 of |x^3-4x^2+3x| ?
The integral from 0 to 3 of |x^3-4x^2+3x| is 37/12