Calculate the area A of the surface given by the parametric equation r(t,θ) = (2t cosθ, 2t senθ, t), 0 ≤ t ≤ 1 and 0 ≤ θ ≤ 2π. The norm of the nor...

Calculate the area A of the surface given by the parametric equation r(t,θ) = (2t cosθ, 2t senθ, t), 0 ≤ t ≤ 1 and 0 ≤ θ ≤ 2π.

The norm of the normal vector ~N is t/√(4t^2 + 1).
The area A is given by the integral ∫(0 to 2π) ∫(0 to 1) t/√(4t^2 + 1) dt dθ.
The integral in t can be solved by the variable transformation u = 4t^2 + 1.
The value of A is π(√53 - 1)/6.
a) Statements 1, 2, and 3 are correct.
b) Statements 1, 3, and 4 are correct.
c) Statements 2, 3, and 4 are correct.
d) All statements are correct.