Question

Consider the parametric equation
x = 3(cos(theta) + (theta)sin(theta)
y = 3(sin(theta) - (theta)cos(theta)

What is the length of the curve for theta= 0 to theta= (5/10)pi?

Answer 1

ds when using polars is something like: sqrt(r^2 + (t')^2)

Answer 2

or we might be able to use: sqrt(x'^2 + y'^2)

Answer 3

t is easier to write instead of theta all the time

Answer 4

x = 3(cos(t) + t sin(t) )
x' = 3(-sin(t)+sin(t)+tcos(t))
= 3t cos(t)


y = 3(sin(t) - t cos(t) )
y' = 3(cos(t) -cos(t)+t sin(t) )
= 3t sin(t)

Answer 5

x'^2 = 9t^2 cos^2(t)

y'^2 = 9t^2 sin^2(t)

add em up

9t^2(cos^2(t)+sin^2(t)) = 9t^2

sqrt(9t^2) = 3t

integrate 3t from 0 to pi/2

Answer 6

Got It! Thanks a lot!