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標題:
line integral
發問:
Compute the line integral of the scalar function f(x,y,z)= 2x^2+8z over the curve c(t)=(e^t,t^2,t) , 0<=t<=3
最佳解答:
?_[0~3) [2e^(2t)+8t]√[e^(2t)+4t2+1] dt = ?_[2~e^6+37] √u du (sub. u=e^(2t)+4t2+1 ) =(2/3) u^(3/2) for u=2~e^6+37 =(2/3)[(e^6+37)√(e^6+37) -2√2]
line integral
發問:
Compute the line integral of the scalar function f(x,y,z)= 2x^2+8z over the curve c(t)=(e^t,t^2,t) , 0<=t<=3
最佳解答:
?_[0~3) [2e^(2t)+8t]√[e^(2t)+4t2+1] dt = ?_[2~e^6+37] √u du (sub. u=e^(2t)+4t2+1 ) =(2/3) u^(3/2) for u=2~e^6+37 =(2/3)[(e^6+37)√(e^6+37) -2√2]
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