Consider the oriented curve C, boundary of a region D, given by C= C1UC2UC3UC4, Where: C1: y = x² – 5x + 4, C2 : x = 4, C3: y= VI y C4 : x = 1 as shown in the following figure: y = Va C = 0D D y = x? – 5x + 4 An expression for calculating the value of (x + y) dx – (x² +y³) dy

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Q: Consider the solid Q bounded by the surfaces: S1 : y = 4 – x², S2: z = 4 – r, S3 : S4 : y = 0 %3D…

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A: Direction of normal always positive y axis. So y component of the normal is positive.

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Q: A possible way for the parameterization of the curve C corresponds to: (9t – t² A) r(t) = , t, z(t)…

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Q: 9) Consider the solid Q in the first octant, generated by the surfaces: x = (y-3)2+ 1, x + 2z = 8, x…

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Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

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Q: 9) Consider the solid Q in the first octant, generated by the surfaces: x = (y-3)²+ 1, x+ 2z = 8, x…

A: We need to use triple integral to find volume

Q: 14. Let f be a continuous function on R2. Consider p2r+2 f(x,y), I = o Jr+1 -dydr I+1 If taken x = u…

A: Ff

Q: S3x² = 16-4z E B S1:2x - 4y +z = 4 DS=aQ S2:2y=6-x S4: x = 0 S5: y = 0 S6: z = 0 0(0,0,0) is the…

A: The given surfaces are: S1:2x-4y+z=4. S2:2y=6-x. S3x2=16-4z Enter the equation of the surfaces as…

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A: From the given information, we have below table:

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Q: 4) Consider the conservative vector field given by: F (x, y) = (y² – ye“, 2xy – e*) A potential…

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Q: 11)Consider the curve C in R3 parameterized by: r(t) = sin(t) î +t² î+3 cos(t) k, con 0 <t < T An…

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Q: Also, suppose that T (x, y) = x³y² + 35 is the function that models the plate temperature in D.…

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Q: 17) Suppose we want to optimize the function V = (x – 1)2 + (y+ 1)² + (z – 1) ², subject to…

A: Option A is true.