Answer to Question #272036 in Calculus for french

Question #272036

Evaluate the line integral ∫ğ’–(ğ‘¥, ğ‘¦, ğ‘§) × ⅆ𒓠ğ¶ , where ğ’–(ğ‘¥, ğ‘¦, ğ‘§) = (𑦠2 , ğ‘¥, ğ‘§) and the curve 𑪠is described by ğ’› = 𑦠= ğ‘’ ğ‘¥ with 𑥠∈ [0,1].


1
Expert's answer
2021-12-15T10:14:48-0500

parameter for of C,

x=t, y=et ,z=et .

r(t)=t i+ et j+et k

=> dr=(i + et j + et k)dt

Then,

"\\int_0^1 u.dr\\\\\n=\\int_0^1 (e^{2t},t,e^{t}).(1,e^t,e^t)dt\\\\\n=\\int_0^1 (2e^{2t}+te^{t})dt\\\\\n=[ e^{2t}+te^{t}-e^t]_0^1\\\\\n=e^2+e-e-1-0+1\\\\\n=e^2"

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