This is another problem my teacher game me.
Given the Polar function r=6*sin(t/2) where the variable t is the angle theta in radians, and that t is between 0 and 2*Pi inclusive. Find the distance around the perimeter of the graph. Hint: this is arc length , round to the nearest integer.
I know to do this to calculate the arc length... it think integrate the equation from 0 to 2[tex]\pi[/tex]
The Attempt at a Solution
integrate(6 sin(t/2) dt, 0, 2pi)
= -12 cos(t/2) ] 0, 2pi
= -12 cos(2pi/2) - (-12 cos(0/2))
= -12 cos(pi) - (-12 cos(0))
= -12 (-1) - (-12 (1)) = 24
I also used f-int in my calculator and got 24. Am I missing a step, what am I doing wrong?