How Do You Calculate Arc Length in Polar Coordinates for r = e^θ?

Mk_ · Feb 28, 2011

Homework Statement

r = e^θ
find arc length from (1,0) to origin

∫ab sqrt (r^2 + (dr/dθ)^2) dθ

∫10 sqrt ((e^θ)^2 + (e^θ)^2) dθ

∫10 sqrt (2(e^θ)^2) dθ

∫10 sqrt (2) (e^θ) dθ

sqrt (2) ∫10 (e^θ) dθ

need help converting limits in terms of theta

uart · Feb 28, 2011

For what value of theta is [itex]e^\theta[/itex] equal to zero?

Mark44 · Feb 28, 2011

Mk_,
uart's question is a bit of a trick question, since e^θ is always positive for any finite number θ.