Use Green's Theorem to evaluate F. ñds, where F =(√x + 3y, 2x + 3y) C is the boundary of the region enclosed by y = 3x - x² and the x-axis (oriented positively).

Q: Find the area of the surface S defined by z = xy and x² + y² ≤ 3. (Use syntax like 2*pi/3)

A: (.)  Given ,  Area of the surface S defined by z=xy and x2+y2≤3 .   If  z=f(x,y) ∀ (x,y)∈R  the…

Q: Let S = Þ (D), where D = {(u, v) : u² + v² ≤ 1, u ≥ 0, v ≥ 0} and Þ (u, v) = (2u+1, uv, 3u + v). (a)…

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Q: Find the area bounded by the two curves f(x) = x² – 8x + 8 and g(x) = - 2² + 6x – 8, and the two…

A: To find Area between two curves:  f(x)=x2-8x+8 and g(x)=-x2+6x-8 and two vertical lines x=3 and x=4.…

Q: Use Green's Theorem to evaluate Jo F = (√x + 5y, 4x + 5y) and C is the boundary of the region…

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Q: A contour map is shown for a function f on the square R = [0, 4] × [0, 4]. Use midpoints with 4…

A: Mid point formula for contour map is  Where is mid point of each rectangle and is area of each…