I'm having trouble finding the point of the maximum curvature of the line with parametric equations of: x = 5cos(t), and y = 3sin(t). I know the curvature "k" is given by the eq.: k = |v X a|/ v^3 Where v is the derivative of the position vector r = <5cos(t), 3sin(t) > , a is the derivative of v, and "v" is the norm of the velocity vector v. I know I first have to find x', x'', y', and y'' to get the vectors v and a, and find the norm of v and cube it. After plugging in the values and taking the absolute value of the cross product above, I evaluated when the numerator of k' (the derivative of the curvature equation) is equal to zero. I came up with the values of arctan(3/5), pi, zero, and pi/2. The book says the the maximum curvature occurs at x = plus or minus 5. I'm not sure what I did wrong. Edit: Additionally, is there any way to integrate the square root of " (25*t^2) + 9 " dt without using integration tables? Any help is appreciated.