Question

f(x,y,z)=xyz, x(t)=(t,2t,3t), 0 15 years ago

Answer 1

is it t from 0 to 2??

Answer 2

f = (t)(2t)(3t)
= 6t^{3}
dx/dt = <1, 2, 3>
\[\left| dx/dt \right| = \sqrt{1^{2} + 2^{2} + 3^{2}} = \sqrt{14}\]
\[ds/dt= \left| dx/dt \right| = \sqrt{14}\]
\[ds = \sqrt{14} dt \]
\[\int\limits_{?}^{?}f ds = \int\limits_{?}^{?}(6t^{3})(\sqrt{14} dt) = (3\sqrt{14}/2) t^{4} + C\]

Answer 3

\[\int\limits_{0}^{2}f ds = (3 \sqrt{14}/2)(16) = 24 \sqrt{14}\]