Let S be the surface which is the graph of a C¹ function f(x, y) defined on an elementary region D. Then the area A(S) of S is given by 11 vi 1 + (f(x, y))² dxdy [ f(x. f(x,y) dxdy af 1² °/L√-CO-C) andy ² dxdy dx 2 2 // √ ¹ + ( )² + ( 2 ) ² 1+ dy 01/√++ 1 + dy f 8 f 2x² dy² dxdy dxdy

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: Find the area enclosed by the graphs of a = f(y) = y³ - 26y + 10 and x = g(y) = 40 - 6y² - y³. (a)…

A: Given:The functions are  and To Find:(a) The intersection point(b) Functions that are to the right…

Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = c² - x² is…

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Q: n exact form. Use symbolic notation and fractions where needed.)

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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: 3) Find the area of the surface formed by revolving the graph f(x) = ;x³ about the x-axis over the…

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Q: Sketch a typical level surface for the function f(x,y,z) = 3x² + 3y² + 3z².

A: Given that the function is                       f(x, y, z)=3x2+3y2+3z2.