Everything is correct except what I put in red color

I put the derivative of x and y in a length formula to get: I'll put "t" for theta

int_0^3/2pi sqrt[(3(tcost))^2 + (3(+tsint))^2]

then i distributed the squares to get:

int_0^3/2pi sqrt[9t^2(cos^2t+sin^2t)]

then i took out the 9t^2 to get:

3 int_0^3/2pi t sqrt[(cos^2t + sin^2t)]

and integrated...

then i took out the 9t^2 to get:

3 int_0^3/2pi t sqrt[(sin^2t + cos^2t)]

I put in t = 3/2pi to get: 29.09768846

Remember that sin^2t + cos^2t = 1

Therefore you get

3 int_0^3/2pi t dt = 3/2 (3pi/2)² = 27pi²/8 = 33.31