The value of _-2^2|3x^2-3x-6|,dx is ..........

Question

The value of $\displaystyle\int_{-2}^2\big|3x^2-3x-6\big|\,dx$ is ..........

Answer: 19

Accepted Answer

$3x^2-3x-6=3(x^2-x-2)=3(x-2)(x+1)$, zero at $x=-1,2$, negative in between on $[-2,2]$:

$$I = 3\int_{-2}^{-1}(x^2-x-2)\,dx+3\int_{-1}^2-(x^2-x-2)\,dx = 19$$

Solutions · 1