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- Line integrals Use Green’s Theorem to evaluate the following line integral. Assume all curves are oriented counterclockwise.A sketch is helpful. The circulation line integral of F = ⟨x2 + y2, 4x + y3⟩, where Cis the boundary of {(x, y): 0 ≤ y … sin x, 0 ≤ x ≤ π}arrow_forwardUsing Stokes' theorem, solve the line integral of G(x, y, z) - (1, x + yz, xy-√z) around the boundary of surface S, which is given by the piece of the plane 3x + 2y + z = 1 where x, y, and z all ≥ 0.arrow_forwardEvaluating a Surface Integral. Evaluate ∫∫ f(x, y, z)dS, where S f(x,y,z)=√(x2+y2+z2), S:x2+y2 =9, 0⩽x⩽3, 0⩽y⩽3, 0⩽z⩽9.arrow_forward
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