Answer
$214200$
Work Step by Step
Need to compute the derivative for the parametric vector equation.
We need to re-write the line integral in terms of $t$ to simplify the integral by using parametric equations.
Now, the line integral is:
$\int_C 2xyz ds=\int_0^1 (2)(12t)(5t)(84t)\sqrt {12^2+25+84^2} dt\\=10080 \int_0^{1} t^3 \sqrt {7225}\\=856800 \int_0^{1} t^3 \ dt \\=214200$
