What is the integral from 1 to 7 of |t^2-2t-15| ?

The integral from 1 to 7 of |t^2-2t-15| is 184/3

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integral from 1 to 7 of |t^2-2t-15|

\int_{1}^{7} t^{2} - 2 t - 15 d t

\frac{184}{3}

Decimal

61.33333 \dots

Solution steps

\int_{1}^{7} t^{2} - 2 t - 15 d t

Eliminate Absolutes

= \int_{1}^{5} - t^{2} + 2 t + 15 d t + \int_{5}^{7} t^{2} - 2 t - 15 d t

\int_{1}^{5} - t^{2} + 2 t + 15 d t = \frac{128}{3}

\int_{5}^{7} t^{2} - 2 t - 15 d t = \frac{56}{3}

= \frac{128}{3} + \frac{56}{3}

Simplify

\frac{128}{3} + \frac{56}{3} : \frac{184}{3}

= \frac{184}{3}

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What is the integral from 1 to 7 of |t^2-2t-15| ?
The integral from 1 to 7 of |t^2-2t-15| is 184/3