Arc Length Question

  • #1

Homework Statement


Find the arc length of r(t) = cos(t)^3 i + sin(t)^3 j
from t = 0 to t = 2 * Pi

It's a hypocycloid that's four cusped.

Homework Equations


[tex]s = \int\sqrt{x'^2 + y'^2}[/tex]


The Attempt at a Solution


x = cos(t)^3
y = sin(t)^3

x' = -3cos(t)^2*sin(t)
y' = 3sin(t)^2*cos(t)

[tex]\sqrt{x'^2 + y'^2}[/tex] = 3* [tex]\sqrt{cos(t)^4*sin(t)^2 + sin(t)^4*cos(t)^2}[/tex]

That simplifies to [tex]s = \int 3*\sqrt{1}[/tex]

So the answer is 6*Pi, but for some reason Maple throws out 6.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
The radical doesn't simplify to 1. Check that again.
 

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