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

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in 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: Evaluate JJ, xy dA, where D is the region bounded by the curves xy = 2,4y = x² and y = 4. а.

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Q: O (y +ev* )dx + (2x + cos y)dy , where C is the boundary of the region enclosed by the parabolas y =…

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Q: 1. Find Sp(r+2y)dA, where D is the region bounded by the parabolas y = r2, and y=1+2

A: I am going to solve the given problem by using some simple calculus to get the required result.

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 : //| cos(x² +y³) dV, where E is the region bounded by the disk x² + y? < 9 E and the plane…

A: From the region of integration which is bounded by x2+y2≤9 and z=1, identify the limits of x, y and…

Q: What is the y=x^2 - 4 and O 1/4 O 1/2 01 03/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

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Q: Evaluate |[(x+2y)dA,where D is the region bounded by the parabolas y= 2x D and y=1+x².

A: We can help you with the question. I am not sure how to help you with its attachments.

Q: Evaluate ffS. Vx² + y² dV, where E is the region tha lies inside the cylinder x? + y² = 16 and…

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

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Q: 3) Evaluate the double integral Sla dr dy where D is the region bounded by the hyperbolas ry = 2, ry…

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Q: 4/ Math

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Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: 3. Use Green's Theorem to evaluate (e3x +y²)dx + (sin y – x²)dy where C is the boundary of the…

A: Green's theorem

Q: Evaluate SS x² y4 dx dy D 1 where D is the region bounded by the hyperbolas xy-2, xyalk parabolas y²…

A: We have to Evaluate the integral  ∬Dx2y-4dxdy where D is the region bounded by the hyperbolas xy=2,…

Q: 1. Find the region in the xy-plane in which the following equation is hyperbolic: [(x-y) -1]u +2uy…

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Q: (z+ y – 1) cos D

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Q: 8. Find the centroid of the region bounded by the given curves, y = x² and r = y?. %D

A: Given that  The curves x=y^2 and y=x^2  To find the centroid of the region

Q: Evaluate ∫∫∫E √x2 + z2dV, where E is the region bounded by the paraboloid y = x2 + z2 and the plane…

A: Given, y=x2+z2 ⇒z2=y-x2z=±y-x2 Therefore the limit of z is -y-x2≤z≤y-x2 On drawing the graph in the…

Q: 8. Use Green's Theorem to calculate f, x?y³dx + (xy - y?)dy where C is the boundary of the region…

A: The given integral is ∫Cx2y3dx+xy-y2dy, where C is the boundary of the region lying between the…

Q: Consider the solid whose base is the region bounded by 4x? + 9y? = 36. Y 3 -3 -2 -1 -1 2 3 2 -3 1.

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Q: Evaluate . (y² z)dV where E be the region in the first octant E bounded by the planes x = z, x + z =…

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Q: Where is the centroid of the region bounded by y = x2, y = 0, and x = 1?

A: First we find the area of the region bounded by the curve area A=∫01f(x) dx=∫01x2…

Q: Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid…

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Q: dA, where R is the trapezoidal region Cos 5. Use appropriate change of variables to evaluate x + y,…

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Q: Use Green's Theorem to evaluate |(e* +y²) dr + (+r²) dy where C is the boundary of the region…

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Q: Evaluate zdV where E is the region under the plane 4x + 2y + z = 4 in the first octant ( E х, у, z >…

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

A: Given area is bounded by x=2y-y2 and y-axis.  On the y-axis, x=0. We try to find the point of…

Q: (2) Consider the region D in the ry-plane which is bounded by the following 2 4 curves y =, y = ỷ =…

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Q: Use Green's Theorem to calculate S,x²y³dx + (xy – y²)dy where C is the boundary of the region lying…

A: Greens Theorem:

Q: (c) Find II zdV where E is the region bounded by the cylinder y² + z² = 9 and the planes E x = 0, y…

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Q: Evaluate x dV , where E is the E region in the first octant bounded by the sphere x² + y² + z² = 1…

A: given region is in the first octant. using spherical coordinates x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ and…

Q: (a) Compute the area of the region R₁ = {(x, y): 1 ≤ x² + y² ≤ 4, x ≤0} using Polar coordinates.

A: a) To Compute the area of the region R1=x, y : 1≤x2+y2≤4, x≤0 using Polar coordinates.

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: 3. Let D be the region bounded by the parabola y= -3 and the line y=1.F

A: The region is bounded by the curves given by: y=x2-3      and      y=1

Q: (a) Calculate the centroid (7, y) of the region under the graph y = cos x for 0 < x <T/2.

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

Q: Verify Green's theorem in the plane for S(3x² -8y )dx +(4y-6xy)dy, Where C is the boundary of the…

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Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

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Q: Evaluate z dV where E is the region bounded between the spheres x² + y² + z² = 1 and x² + y? + z° 4…

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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: Let D be the solid region in the first octant bonded above by z-3 and below by 2= 2++y. Then the…

A: Here we will have to project the 3-dimensional solid regions on a 2-dimensional plane. Hence, we…

Q: where E is the region bounded by the paraboloid y= r+ z2 (Figure 15.4. %3D y = x2 + z?

A: Please rate and feel free to ask any query about any part of the question .

Q: 3. Use Greens theorem to evaluate (e* + y²)dx + (e' + x²) dy where c is the boundary of the region…

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Q: Verify Green's theorem in the plane for (3x² -8y²)dx+(4y-6xy)dy, where C is the closed curve of the…

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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 line integral [2y'dx+(x* +6y°x)dy where C is the boundary of the R region shown below…

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