3. Explain what is wrong with the following statement: If R is the region 0≤x≤ 1,0 ≤ y ≤ 4 and T is the region 0≤ s≤ 1,-2 ≤ t ≤ 2, using a = s, y = t2, we have f(x, y)dady = [ f(s, SR R t²) |(x, y) | a(s, t) dsdt

Q: Evaluate Sf xydA, where D is the region bounded by y = x - 1 and y² = 2x + 6

A:

Q: Given that p, = x² +xy, calcultae p, ds, over the region, y <x,0 <x < 1.

A:

Q: •/F. Evaluate F. dr. F(x, y) = xi + yj C:r(t) = (9t + 1)i + tj, 0sts1

A:

Q: SZ Let x, y, z=R with x≤z. Show x≤ y ≤z if and only if lx-yl+ ly-z=1x-z1.

A:

Q: 23. Let D denote the region of the plane between the circles x² + y² = 1 and a² + y² = 4, and above…

A:

Q: 1. Find the area of the enclosed region by y= 6-x,y= v and line y = 0. %3D 2. Find the area of the…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Calculate ffs f(x, y, z) dS For y = 5 - z², 0 < x, z≤6; f(x, y, z) = = N s f(x, y, z) ds =

A: The objective of this question is to calculate the surface integral of a function f(x, y, z) over a…

Q: Evaluate fe (2x – 2y),/x+ y dA x+y = 3. where R is bounded by y = x, y = x – 1, x + y = 0, and

A: Given:

Q: Calculate ffs f(x, y, z) ds For Sfs f(x, y, z) ds = x² + y² =9, 0≤ z ≤ 9; f(x, y, z) = e

A:

Q: Calculate ffs f(x, y, z) dS For y = 5 - z², 0 < x, z≤6; f(x, y, z) = = N s f(x, y, z) ds =

A: To evaluate the surface integral (∬S​f(x,y,z)dS) over the surface (S), where (S) is defined by (y =…

Q: Calculate fff(x, y, z) dS For s f(x, y, z) ds x² + y² = 16, 0≤ z < 2; f(x, y, z)=e*

A:

Q: If S√√ƒ(² (b) If f(x, y) dA=0 then f(x, y) = 0 for every (x, y) in the region R.

A: (b) If  then  for every  in the region .To check: The correctness of the above statement.

Q: Evaluate cxy)dA av)d4 over the region R bounded by y = 2r, y=x+1 and x = 3. (3, 6) 5.5+ y-2x 4.5+…

A:

Q: Calculate Js f(x, y, z) dS For Is f(x, y, z) ds = y = 7-z², 0≤x, z ≤7; f(x, y, z) = = Z

A:

Q: What is P {Y ≤ <}}? f(x, y) = { (4x + 2y) 3 0, ) 0≤x≤ 1,0 ≤ y ≤ 1 elsewhere

A: fxy(x,y)=4x+2y3,0≤x≤1,0≤y≤10,otherwise we have to find PY≤12

Q: 3. Evaluate ff 2x + 5y dA over the region given by D = {(x,y)| 0≤x ≤ 1,x³ Sy, Sx³ + 1}

A:

Q: 3- calculate SSm xe' dxdy -if the bounded set M is given by inequalities y <2 - x, y 2 x². -Draw the…

A: The region y≤2-x isThe region y≥x2  is The region M is,

Q: Work done by the force F(x,y) = (3x² +3e-7+(-4y²-3xe - acting along the curve y = x³ for 0≤x≤l is…

A:

Q: Problem & (3 points). Complete the definition of a metric space by filling in the three blanks: A…

A: Given: The incomplete statement about the metric space.We need to fill in the three blanks by…

Q: Evaluate • Sf. dr. 1 F(x, y) = xi + yj C: r(t) = (5t + 1)i + tj, X 0 st≤ 1

A:

Q: 2- Find D xyz dV where D is the region with -1 ≤x≤1, x ≤ y ≤ 1, above z = x, and below z = y + 2.

A:

Q: Calculate f(x, y, z) dS For Is f(x, y, z) ds = y=9-z², 0≤x, z≤ 8; f(x, y, z) = z

A:

Q: 3) Evaluate X $1₂₁ + x² D = {(x, y)|0 ≤ y ≤ x², 0≤x≤ 2} dA where D=

A: The given problem is to Evaluate the given double integral over the given region D={(x,y)|…

Q: 37. Evaluate JJ(x +y)dA over the region R, as shown below.

A: Follow the procedure given below.

Q: Suppose region E is between two hemispheres of radius 2 and radius 5 above the xy-plane. Set us and…

A:

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Q: Evaluate S[(z+ y)² dA R where R is the region enclosed by the lines z +2y = 0, r+ 2y = 4, x – 2y =…

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Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: [S (x - 2y + z) ds. S: z = 6 x, 0≤x≤ 6, 0≤ y ≤ 5 Evaluate

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Q: te /// (+ (xy + yz + xz)dV B B = {(x, y, z) | 0≤x≤ 10,0 ≤ y ≤ 7,0 < z < 1}. Evaluate

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Q: Let W ~ Bin(2, p) and X ~ Bin(4, p). If P(W > 1) = 0.33, find P(X > 1)

A:

Q: 2. Compute ¡ E x dV , where E “ tpx, y, zq | x ď 0, z ď 0, x2 ` y 2 ` z 2 ď 9u

A: The given integral,

Q: Evaluate ǝw (x, y, xz) ds where W = {(x, y, z) : x² + y² ≤ z ≤ 1}.

A: In the given problem we have to evaluate:∫∫∂W​⟨x, y, xz⟩⋅dSwhere:W={(x,y,z):x2+y2≤z≤1}Now using the…