What is the integral from 0 to 3 of |t^2+4t-5| ?

The integral from 0 to 3 of |t^2+4t-5| is 52/3

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integral from 0 to 3 of |t^2+4t-5|

\int_{0}^{3} t^{2} + 4 t - 5 d t

\frac{52}{3}

Decimal

17.33333 \dots

Solution steps

\int_{0}^{3} t^{2} + 4 t - 5 d t

Eliminate Absolutes

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

\int_{0}^{1} - t^{2} - 4 t + 5 d t = \frac{8}{3}

\int_{1}^{3} t^{2} + 4 t - 5 d t = \frac{44}{3}

= \frac{8}{3} + \frac{44}{3}

Simplify

\frac{8}{3} + \frac{44}{3} : \frac{52}{3}

= \frac{52}{3}

What is the integral from 0 to 3 of |t^2+4t-5| ?
The integral from 0 to 3 of |t^2+4t-5| is 52/3