1. The problem statement, all variables and given/known data Vector calculus It can be shown that the area of the surface described by the vector valued function r(s; t) between the limits a ≤ s≤ b and c ≤ t ≤ d is given by A=∫(from a to b) ∫(from c to d ) ‖(∂r/∂s)×(∂r/∂t)‖ dtds Find the surface area of the bowl described by r(s; t) = s cos(t)i + s sin(t)j + s^(2)k; 0 ≤ s ≤ 1; 0 ≤ t ≤ 2π: 2. Relevant equations 3. The attempt at a solution Ok so first off I've solved this problem but am unsure if I am correct. The final answer I came to is roughly 50. However my friend thinks its roughly 5.33. I'm sure he is incorrect because in the last few steps the integral required a u substitution, where he didn't change the limits of integration in this case instead of 1 to 0 the new limits became 5 to 1. if someone could check this I would be greatly appreciative. thanks for your help.