(b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y² with dV = dz dy dr.

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

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

Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x – y) dy for the given path. C:…

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Q: (2y – x*)dx + (4x + y²)dy where C is the boundary of the region in first quadrant bounded by x2 – 2x…

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Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

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Q: Determine a region of the xy-plane for which the DE (y- x) y' = y+ xwill have a unique solution…

A: Consider a differential equation y'=F(x,y), y(x0)=y0. Then there exist a unique solution to this…

Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

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Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

Q: D Evaluate xy dady where D is Hie region bounded x=0, y=0, and x+y= ! by

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Q: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: Evaluate y'dx+ xydy where C is the boundary of the region bounded by y = Vx.y 0, and x 9.

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Q: Evaluate (2r+y) dV _ where V is closed region bounded by the z= 4>x and the planes x = 0, y = 0 and…

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Q: Use Green's Theorem to evaluate the line integral. |v² dx + xy dy C: boundary of the region lying…

A: Introduction: The line integral ∫CF·dr geometrically represents the circulation of the function F…

Q: Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose…

A: Theorem of existence of uniqueness: If f(x,y) and dfdy are continuous on rectangular region R, then…

Q: Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C:…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: y2 %3D 1. 60. x²y dx dy dz, T: Region bounded by 4

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Q: Use Green's Theorem to evaluate the line integral. dx + xy dy C: boundary of the region lying…

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Q: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

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

Q: Evaluate the moment M, and My of the region bounded by x = 2y – y² and the y=axis.

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Q: Q1 Verify that [Oy²-2x )dx +(2xy +x² xdy = [[ ƏP dA where C is the boundary of a region R R defined…

A: We have to verify ∫Cy2−2xdx+2xy+x2dy=∬R∂Q∂x−∂P∂ydA, where C is the boundary of a region R defined by…

Q: 4. Evaluate fe cosy dx + (xy – xsiny) dy where C is the boundary of the region lying between the…

A: Given  ∫Ccosydx+(xy-xsiny)dy

Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

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Q: Q3 Verify Green's theorem in plane for (x² - 2xy) dx + (x²y + 3)dy where c is the boundary of the…

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Q: Evaluate (x+ y) dx +xy dy, where Cis the positively-oriented boundary of the region bounded by the…

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + ху dy C: boundary of the region lying…

A: Use green s theorem

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.

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Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the %3D Vr2 + y? with…

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Q: ]]] xyz dV if S is the region bounded above by x² + y² +2²= 16 and below the S cone 2 = √² + y² with…

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Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy for the given path. C:…

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Q: Evaluate the moment M, and M, of the region bounded by x = 2y - y2 and the y=axis.

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Q: (b) || 6xy dV, where E lies under the plane z 1+x + y and above the region in the xy-plane bounded…

A: A triple integral involves the integral with respect to x,y, and z. In this problem, we have to…

Q: Evaluate the triple integral. 8z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x…

A: Please refer the attached image for complete solution.

Q: Evaluate || Vx2 +y? dx dy over the region R in the xy plane bounded by x² +y² = 36 - R

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Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x - y) dy for the given path. C:…

A: Use greens theorem

Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

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Q: Use Green's Theorem to evaluate the line integral √(x − x) dx + (2x - y) dy (y- for the given path.…

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Q: Use Green's theorem to evaluate the integral: 6(-x²y)dx + xy°dy where C is the boundary of the…

A: Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region…

Q: 17. (2 +y +2) dx dy dz, W is the region bounded W by x+y+z= a (where a> 0), x = 0, y= 0, and z= 0.

A: We have to solve the integral and show the graph of question 17.

Q: x² and t %3D 2) = z where E is the region bounded by the parabolic cylinder y

A: We have to set up the integral according to the given information

Q: | 5z2 dV , where E is Evaluate E the region bounded below by the cone z = Vx2 + y² and above by the…

A: Given: ∫∫∫E5z2dvz=x2+y2x2+y2+z2=1

Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

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Q: Verify that [y- 2x )dx +(2xy +x²)dy = dA where C is the boundary of a region %3D R R defined by y=0,…

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Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy for the given path. C:…

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Q: Evaluate (x+ y)dx+ xy dy. where Cis the positively-oriented boundary of the region bounded by the…

A: We have to evaluate the integral                                                  ∮Cx+ydx+xydy Where…

Q: Use Green's Theorem to evaluate (e" + y²) dx+ (e" +x²) dy where C is the boundary of the region…

A: we have to evaluate the following by using greens theorem

Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

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Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

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