問兩題線積分

1. ∫ x(e^yz) ds . 【Ｃ is the line segment (0,0,0) to (1,2,3)】

Ｃ



2. Use Green Thm. to evaluate ∫ (e^y)dx 2x(e^y)dy .

Ｃ

【Ｃ is the square with x=0 to x=1; y=0 to y=1】





Solve:



1. x=t

y=2t 0≦t≦1

z=3t



代入



1

∫t(e^6t^2)√(1 4 9) dt

0



=√14/12(e^6-1)