Second example of line integral of conservative vector field

Closed curve line integrals of conservative vector fields

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

Calculating The Line Integrals of Vector Fields

Scalar field line integral independent of path direction Video Lecture - Chemical Engineering

Difference between conservative and non conservative field... | Filo