推 zxc95 :謝謝你:) 04/18 19:27
※ 引述《zxc95 ()》之銘言：
: Compute ∫F dx for the following F and C :
: c
改這樣好了 ∫F dX X代表向量
: (a) F(x,y,z)=(yz,x^2,xz); C is the line seqment from (0,0,0) to (1,1,1).
X=(t,t,t) 0 <= t <= 1
dX = (1,1,1)dt
原式 = ∫(t^2,t^2,t^2) (1,1,1) dt t屬於[0,1]
內積
: (b) F is as in (a); C is the portion of the curve y=x^2 ,
: z=x^3 from (0,0,0) to (1,1,1).
X = (t,t^2,t^3) 0 <= t <= 1
dX = (1,2t,3t^2)dt
原式 = ∫(t^5,t^2,t^4) (1,2t,3t^2) dt t屬於[0,1]
內積
: 答案:(a) 1 (b) 23/21
: 跟我算的不一樣,想請教高手!!
: 謝謝~
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