SOLVED: 3. Find a potential f of the given vector field 𝐅 and use the potential in conjunction with the fundamental theorem of line integrals to evaluate ∫𝒞𝐅∙ d 𝐫 along the given path.𝐅(x, y)=(1 x y) e^x y𝐢 x^2 e^x y𝐣 and 𝒞 is given by the image of the vector valued function 𝐫(t)=cos (t) 𝐢 2 sin (t) 𝐣, and 0 ≤ t ≤(π)/(2)Recall the Fundamental Theorem of Line Integrals asserts that ∫𝒞𝐅∙ d 𝐫 = =∫𝒞∇ f ∙ d 𝐫 =f(r(b))-f(r(a))when it is applied to a conservative ve
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