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

The integral from 2 to 4 of |t^2-2t-3| is 4

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integral from 2 to 4 of |t^2-2t-3|

\int_{2}^{4} t^{2} - 2 t - 3 d t

4

Solution steps

\int_{2}^{4} t^{2} - 2 t - 3 d t

Eliminate Absolutes

= \int_{2}^{3} - t^{2} + 2 t + 3 d t + \int_{3}^{4} t^{2} - 2 t - 3 d t

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

\int_{3}^{4} t^{2} - 2 t - 3 d t = \frac{7}{3}

= \frac{5}{3} + \frac{7}{3}

Simplify

\frac{5}{3} + \frac{7}{3} : 4

= 4

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What is the integral from 2 to 4 of |t^2-2t-3| ?
The integral from 2 to 4 of |t^2-2t-3| is 4