8. (8 points) Find the function f if ∇f=⟨3x2y+y2,x3+2xy⟩, and evaluate the integral ∫C​∇f⋅dr with and without the Fundam

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8 8 Points Find The Function F If F 3x2y Y2 X3 2xy And Evaluate The Integral C F Dr With And Without The Fundam 1 (24.49 KiB) Viewed 33 times

8. (8 points) Find the function f if ∇f=⟨3x2y+y2,x3+2xy⟩, and evaluate the integral ∫C​∇f⋅dr with and without the Fundamental Theorem of Line Integral, where C is the curve r(t)=⟨2t,5t⟩,0≤t≤1. 9. (8 points) Let F be the vector field defined by F(x,y)=⟨3x+5y,−x2+7y⟩. Evaluate the following line integral with and without Groen's 'Theorem. ∫C​p​⋅dr, where C is the positively oriented triangle bounded by the axes and the line x+y=3.