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

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

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

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

1

Solution steps

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

Eliminate Absolutes

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

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

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

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

Simplify

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

= 1

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