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

[Mk_]

Homework Statement

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

Homework Equations

∫ab sqrt (r^2 + (dr/dθ)^2) dθ

The Attempt at a Solution

∫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]

For what value of theta is $e^\theta$ equal to zero?

 

[Mark44]

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