设L为：x=1,0≤y≤3/2的弧段,则∫(L)6ds等于多少?

Question

设L为：x=1,0≤y≤3/2的弧段,则∫(L)6ds等于多少?

Answer 1

∵x=1,则dx=0
∴ds=√[(dx)²+(dy)²]=dy
又0≤y≤3/2
故∫(L)6ds=6∫dy
=6(3/2-0)
=9.