|| | /3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8. %3D

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: Evaluate ∭E sqrt(x2+y2) dV where E is the region that lies inside the cylinder x2+y2=4 and between…

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

A: Solution :-

Q: 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the…

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Q: The area bounded by the curve z 4y+7, the y-ax y =0 and y 2 is dy3D O 18 22 11 O 15

A: Area bounded by the curve can be calculated as

Q: 70. Solid bounded above by x² + y² + z² = 36 and below by = 2 Vx + y?

A: Given: Consider The volume of any solid E in R3

Q: 5xy dv, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by…

A: The given integral is ∭E5xydV. The region E lies under the plane z=1+x+y and above the region in the…

Q: 3 The triple integral L (x + 2y – z)dxdydz is equal to

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Q: Supply the missing integrand and the limits of integration x dx dy V4 + x² _dy %3D

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Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

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Q: Evaluate: ∬ 〖4X d A〗 over the region R bounded by the parabola Y = X ^ 2 and the line X = Y-2.

A: Plotting the Curves on X and Y-axis : y = x2 ...............(1)y = x + 2 ..............(2)After…

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = S [² f(x) dx + √° 9( g(x)…

A: Given the region is bounded by y = x3 , y = 2x+4 and y = -1. Intersection of y = x3 and y = 2x+4 is…

Q: The numerical value of f3dA 3dA (where D is the region bounded by lines y=0 and x= 1 and the…

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Q: (iii) Sf xy²e*dA, Dis bounded by y = x,y = 2,x = 0.

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Q: 1. Evaluate , 3y e ²x dA where D is the region bounded by x = ₁x = 1, y = 1 and y = 2. 2

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Q: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw…

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Q: 10. Swap the order of integration for Só Sà f(x,y)dydx.

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Q: Supply the missing integrand and limits of integration. (3x² – 2xy + y³) dx dy = .dy (36–4y)dy (56–…

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Q: Evaluate the triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

Q: The area of the region between the curve y = xr? – 6x +8 and the x-axis & r = 0 ; x = 3 is given by…

A: here option c is true because we will take the area in x -axis so will take limit of x and integrate…

Q: Supply the missing integrand and limits of integration. dy (3x² – 2xy + y³) dx dy

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Q: Evaluate the integral: 1. - 1 (1- 5x + x³ – 2x5 5х + x3 — 2x5 dx x2 2. S(y³ – 3,/y+ Vy) dy

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Q: Q4) Use the Jacobian to evaluate ( sin (x +3y) xdy where 1+(x - y) 2 is the region enclosed by: x…

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Q: B)evaluate the line integral: $5xy'dx- dx +x'ydy where c: y = x; y= x

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Q: 2. Sketch the region of integration and reverse the order of integration. S " f(x, y)dydx

A: see 2nd step

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: Evaluate 7x dV where E is the region that lies inside the cylinder x2 + y² = 8 E and between the…

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Q: +5y )dx+(2x-4y) dy edary of the region lying between

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Q: Evaluate fff 12y - 8x dV wherein the limits of integration are the region behind y = 10-2z and in…

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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: 5. Evaluate z dV where E is the region bounded below by r2 +y² + z² = 4 and above %3D by r² + y² +…

A: We have to evaluate the integral ∭EzdV, where Eis the region bounded below by x2+y2+z2=4 and above…

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the…

A: The objective is to evaluate the triple integral ∫∫∫E8xdV, where E is bounded by the paraboloid…

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: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: The value of (4xy- (sinx)³)dx + (x² + y9)dy (Correct to ONE decimal place) where C is the region…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. To evaluate the given…

Q: 1 Integrate the function f (x, y) = over the region bounded by r-axis, line æ = 7, and the curve y =…

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Q: O R is the region bounded by y = 2 – x² and y = x² – 6. - %3D

A: 5.)  y=2-x2  and  y=x2-6 red line y=2-x2 blue line y=x2-6

Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

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Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the…

A: here, E is bounded by the paraboloid  x=7y2+7z2  and the plane x=7.    so , at    x=7 ,     y2+ z2…

Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and the…

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Q: Find the partial integral. (3х + 5y) dx

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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,   4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and…

A: To calculate the value of the triple integral under the given terms

Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: Evaluate [ sin (3x +3y)dA where D is the region between x +y' 1 and x+y 7.

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Q: 2 + xy DA where R is bounded by y = 3 - Vx, x= 3 2y

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Q: 3. Evaluate SIS 3z dV where E is the region inside both x² + y² + z² = 1 and z = E x² + y².

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Q: Set up the triple integral 8y dV, where E is bounded by the coordinate planes and the plane x + y +…

A: To Set up the triple integral for 8y dV, where E is bounded by the coordinate planes and the plane x…

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

A: