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 = 3/2(pi)?

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 sqrt[(cos^2t + sin^2t)]

and integrated...

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

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

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

my online submission was declared incorrect. Can anybody help me see what I did wrong?

Thanks!