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Find the total distance traveled over the time interval 0 <= t <= 4 by an object moving along a curve in the x-y plane whose velocity is...?
Find the total distance traveled over the time interval 0 <= t <= 4 by an object moving along a curve in the x-y plane whose velocity at any time t is dx/dt = arctan(t)/(1 + t) and dy/dt = ln(t^2 + 1).
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- ?Lv 77 years ago
ds = √[(dx/dt)^2 + (dy/dt)^2] dt
S = {t: 0 to 4}∫√{[arctan(t)/(1 + t)]^2 + [ln(t^2 + 1)]^2}dt
Not immediately obvious how to simplify & integrate; perhaps use online software
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