What is the integral of f (x, y, z) = 4 y2 + 5 y z over the region bounded by –12 x +8 y – 2 z= -38, 3 x – 2 y – 9 z= -38 , 16 z + 2 y – 10 z = 38, –12 x + 8 y – 2 z= 0, 3 x – 2 y – 9 z = 0 , and 16 x + 2 Y – 10 z = 0?

Q: - dA = in( Show that, in the region D: 0 < x <1, 0<y< x², the following double integral y dA x5 + 1…

A: Given the integration ∫∫Dyx5+1dA and the region D: 0≤x≤1, 0≤y≤x2

Q: The following line integral is path independent in the space and r(0,2,5) S (2xdx + sin z dz + y cos…

A: The line integral of a vector field, F→ along C can be defined as ∫CF→⋅dr→ .

Q: Suppose that f(x, y) = ²/" on the domain D = {(x, y) |0 ≤ y ≤ 1,0 ≤ x ≤y³}. D Then the double…

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Q: Q3: What is the answer of the double integral of the f (x, y) = 4x+2 over the region x^2<ys2x, and…

A: According to question, Given function,fx, y = 4x+2,x2 ≤y≤2x,0 ≤x ≤ 2

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A: The double integral ∬Rfx, ydA can be written as ∬Rfx, ydxdy. We have given the rectangular region as…

Q: 9. Compute each of the following double integrals over the indicated rectangles. 1 dA, (2л + 3у)2 R=…

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Q: 1. Evaluate the integral: I = 2x drdydz where the solid S is defined as: S = {(r, y, z) E R³:x > 0;…

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Q: Suppose that f(x, y) = x +y on the domain D = {(x, y) | 1 ≤ x ≤ 2, x² ≤ y ≤ 4}. D Then the double…

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Q: Evaluate the double integral of f(x, y) = Vx2 + y2 over the triangular region with vertices (0, 0),…

A: We will find out the required double integral.

Q: Determine the Riemann integral partitions given by Pn = Qn = {o, 0, 1 4 1 2 4n' 4n 3+n " 6 + 2n 4n…

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Q: 1. The integral of J, \z|dz along any closed path y is 0.

A: As per our guidelines, we suppose to answer only one question in case of multiple questions posted.…

Q: Compute the double integral of f(x, y) = (x + y)- over the region bounded by y = x, y = 1, y = e,…

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Q: 19-9z Set up the iterated double integral S dy da as dxdy such that: ( 0 0 i. the limits of x ( ii,…

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Q: Let f(x, y) = 3x² + 2y² – 2xy — 1. Find the local maximum and minimum values and saddle points of f,…

A: Double derivative test if (a, b) is the critical point of z=f(x,y) and D=fxxa, bfyya, b-fxya, b2…

Q: Compute the integral of f(x, y, z) = y2 over the region within the cylinder x 2 + y2 = 4, where 0…

A: Given f(x,y,z)=y2

Q: Evaluate f z2 In z dz using integration by parts O 22 In z – +c 12 O In z - +c O 22 In z-폭 +c O In z…

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Q: 3. A) Evaluate the triple integral xdV, where E is the solid region bounded by the cylinder 4 = y =…

A: 3.A) The given integral is      ∫∫∫E x dV , E is the solid bounded by x2+y2=4, z=0, y=3z, x=0 and in…

Q: 19 9r Set up the iterated double integral S S dy dæ as dxdy such that 0 0 i. the limits of x ii. the…

A: solution is given below

Q: 2) Evaluate the following line integral:S. (v + z)dx + (x + z)dy + (x + y)dz where C consists of the…

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Q: Let f(x, y) = 3x² + 2y² − 2xy — 1. Find the local maximum and minimum values and saddle points of f,…

A: Double integral, Maxima minima

Q: Example: 1. Evaluate the double integral SRS (3y – 2x2)dA if R is the region consisting of all…

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Q: Suppose that f(x, y) = √√/4² -2² - y² on the domain D = {(x, y) | x² + y² ≤ 4²}. Q Then the double…

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Q: Suppose that f(x, y) = 7x + ly at which {(x, y) | – 4 < a < 3, – 4 < y< 3}. D Then the double…

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Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y² ≤ 4}. I Then the double integral of f(x, y) over…

A: Explanation of the answer is as follows

Q: 25. Evaluate the integrals. (a) |(*+y) d4, D bounded y =Vx and y= x. (b) [[[yz cos(x' HV where E =…

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Q: 1) Evaluate the triple integral SS, f(x,y, z)dv : A) f(x,y, z) = 2x + y – z, Q = {(x,y, z): 0 < x, z…

A: A) Set up the triple integration using the given information.Here dv represents dxdydz.…

Q: The double integral R f(x, y) dA over the region R = {(x, y)| - 2< x < 2, x - 8 < y< -x²} can be…

A: Given integral is ∬Rfx,ydA over the region  R=-2≤x≤2x2-8≤y≤-x2 The limits and order of the…

Q: #2. Evaluate the double integrals (a) || xyVx² + y² dA, R where R= {(x,y):0<x< 1, 0< y< 1}. (b) |…

A: We have to find the integral for given question       According to our guidelines, we can solve only…

Q: Suppose that f(x, y) = 1x + 3y at which {(x, y) | 1 < x < 2, x² < y < 4}. D Then the double integral…

A: Solution: The objective is to evaluate the double integral

Q: (1) Evaluate the line integral of F (x, y) = (x – y, x²) over the line from (1,0) to (3, 2). |

A: evaluate line integral in following way

Q: Suppose that f(x, y) = 5x + 5y on the domain D = {(x, y) | 1 < x < 2, x² < y< 4}. D Then the double…

A: ∬f(x,y) dxdy=∬f(x,y)dydx

Q: 9. Compute each of the following double integrals over the indicated rectangles. 1 J/ 2+ 3y)adA, R=…

A: I can solve using separation of variables.

Q: What is the integral of f (x, y, z) = 5 x y+ 5 z over the region bounded by –12 z + 28 y + 19 z =…

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Q: 60. Calculate the integral of f(x, y) = e3x=2y over the parallelogram in Figure 7. (6, 4) |(1, 3) D…

A: Consider the given integral, fx,y=e3x-2y consider the given parallelogram in the figure, the…

Q: Suppose that f(x, y) D = {(x, y) | x² + y² < 9}. 6, and Then the double integral of f(x, y) over D…

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Q: Compute the double integral of f(x, y) = 18xy over the given shaded domain in the following Figure :…

A: Given fx,y=18x5y

Q: The double integral ff 2xy³dA over the rectangular region R = {(x, y) E R², 0<x<4 and–1<y<0}is equal…

A: Given that, I=∬2xy3dA and  0≤x ≤4  and  -1≤y≤0 here dA = dxdy

Q: 1.) Set up the integral ||[ f (x,y,z)dV using a single triple integral where E is E the solid in the…

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Q: Suppose that f(x, y) = e² / Y on the domain D = {(x, y) | 0 < y < 2,0 < x < y³}. D Then the double…

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Q: 2) Evaluate the following line integral:S, (y + z)dx + (x + z)dy + (x + y)dz where C consists of the…

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Q: B. Verify Green's Theorem by evaluating both integrals involved in that theorem when F = (x² – y) i+…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the closed region D. The Green's…

Q: 13. Find the double integral ff(62²-4zy) dA, where R is the region bounded by y=2² and y=z.

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Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y? < 4}. Then the double integral of f(x, y) over D…

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Q: 2. Evaluate the iterated integrals by (i) viewing R as a type I region, and/or (ii) viewing R as a…

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Q: Suppose that f (x, y) = 8x + 7y at which {(x, y) | – 2 < x < 3, – 2 < y < 3}. - D Then the double…

A: Use the integrating limit given on the set separately for x aand y

Q: Evaluate the triple integral of f(x,y,z)=z(x2+y2+z2)−3/2f(x,y,z)=z(x2+y2+z2)−3/2 over the part of…

A: Consider the provided question,

Q: 9. Calculate the triple integral of the function f (x, y, z) = e-(æ²+y²)(1–æ²–y²) over the region B…

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Q: Let f(z)=4Re(z) and C be the line segment connecting 1+i to 0. Then the integral of f over C is…

A: Given function is fx=4Rez and C be the line segment connecting 1+i to 0 We have to find the integral…