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

The integral from 0 to 2 of |x^3-3x^2+2| is 5/2

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

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

\frac{5}{2}

Decimal

2.5

Solution steps

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

Eliminate Absolutes

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

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

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

= \frac{5}{4} + \frac{5}{4}

Simplify

\frac{5}{4} + \frac{5}{4} : \frac{5}{2}

= \frac{5}{2}

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What is the integral from 0 to 2 of |x^3-3x^2+2| ?
The integral from 0 to 2 of |x^3-3x^2+2| is 5/2