一題向量微積分

S can be parametrized as r=(x,y,z)=(s cost, s sint, t), 0<=s<=1, 0<=t<=2π
∂r/∂s=(cost, sint, 0), ∂r/∂t=(-s sint, s cost, 1)
dA=| (∂r/∂s)x(∂r/∂t)| ds dt (cross product)
=| (sint, -cost, s)| ds dt=√(s^2+1) ds dt
so, Area=∫[0~2π]∫[0~1]√(s^2+1) ds dt
=0.5∫[0~2π] [s√(s^2+1)+ln| s+√(s^2+1) | ]|[0~1] dt
=0.5∫[0~2π] [√2+ln|1+√2|] dt
=π[√2+ln(1+√2)]

恭喜天助大升大師五級~~~~~~~~