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

The integral from 0 to 2 of |-x^2+3x-2| is 1

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

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

1

Solution steps

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

Eliminate Absolutes

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

\int_{0}^{1} x^{2} - 3 x + 2 d x = \frac{5}{6}

\int_{1}^{2} - x^{2} + 3 x - 2 d x = \frac{1}{6}

= \frac{5}{6} + \frac{1}{6}

Simplify

\frac{5}{6} + \frac{1}{6} : 1

= 1

\int_{- 2}^{2} ∣ x + 1 ∣ d x

\int_{1}^{0} ∣ 2 x - 1 ∣ d x

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

\int_{- 1}^{1} \frac{1}{x ^{2} - 4} d x

\int_{1}^{e^{2}} \frac{( ln ( x ) ) ^{2}}{x} d x

What is the integral from 0 to 2 of |-x^2+3x-2| ?
The integral from 0 to 2 of |-x^2+3x-2| is 1