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 46/3

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

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

\frac{46}{3}

Decimal Notation

15.33333 \dots

Solution steps

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

Eliminate Absolutes

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

\int_{- 2}^{- 1} t^{2} - 2 t - 3 d t = \frac{7}{3}

\int_{- 1}^{3} - t^{2} + 2 t + 3 d t = \frac{32}{3}

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

= \frac{7}{3} + \frac{32}{3} + \frac{7}{3}

Simplify

\frac{7}{3} + \frac{32}{3} + \frac{7}{3} : \frac{46}{3}

= \frac{46}{3}

f^{^{'}} (x) = 2 x^{2} + 3 x - 2

\frac{\partial}{\partial x} (x^{4} y - x^{2} y^{3})

y = 3 x^{2} + \frac{4 x}{3} - 2

\frac{3}{r ^{3}}

\frac{d y}{d x} = \frac{1 - y ^{2}}{x}

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 46/3