APFIVE Distance Traveled Versus Displacement Magnitude
A particle moves with velocity vector $$\vec{v}(t) = \langle e^t,\ te^t \rangle$$. If the particle is at the origin when $$t = 0$$, what is the difference between the total distance traveled and the magnitude of displacement from $$t = 0$$ to $$t = 1$$?
A
$$e - 1$$
B
$$e\sqrt{2} - \sqrt{2}$$
C
0
D
$$\int_0^1 e^t\sqrt{1+t^2}\,dt - \sqrt{(e-1)^2+1}$$
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