What is the integral from 1 to 5 of |t^2-2t-8| ?

The integral from 1 to 5 of |t^2-2t-8| is 64/3

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integral from 1 to 5 of |t^2-2t-8|

\int_{1}^{5} t^{2} - 2 t - 8 d t

\frac{64}{3}

Decimal

21.33333 \dots

Solution steps

\int_{1}^{5} t^{2} - 2 t - 8 d t

Eliminate Absolutes

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

\int_{1}^{4} - t^{2} + 2 t + 8 d t = 18

\int_{4}^{5} t^{2} - 2 t - 8 d t = \frac{10}{3}

= 18 + \frac{10}{3}

Simplify

18 + \frac{10}{3} : \frac{64}{3}

= \frac{64}{3}

\int_{0}^{1} \frac{( x ^{2} )}{x ^{2} + 1} d x

\int_{x}^{1} \frac{1}{t} d t

\int_{- 3}^{1} e^{x + 3} d x

\int_{0}^{- 1} x e^{- x} d x

\int_{0}^{\frac{π}{2}} cos^{3} (2 x) d x

What is the integral from 1 to 5 of |t^2-2t-8| ?
The integral from 1 to 5 of |t^2-2t-8| is 64/3