Answer
$\dfrac{7 \sqrt 3}{3}$
Work Step by Step
The formula to calculate the arc length is as follows: $L=\int_{c}^{d} \sqrt {1+[f'(x)]^2} dx$
Re-write the equation as follows:
$L=\int_{-2}^{-1} \sqrt {3x^4} dx$
Separate the terms and integrate as follows:
$L= \sqrt 3 \int_{-2}^{-1} x^2 dx \\= \sqrt 3 (\dfrac{x^3}{3})_{-2}^{-1} \\= \dfrac{7 \sqrt 3}{3}$
