b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane defined by Osxs 2,0s y s1.

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 p (x² – 2xy)dx + (x²y +3)dy around the boundary of the region defined by y? = 8x and x = 2…

A: To evaluate : ∮x2-2xy dx+x2y+3 dy around the boundary of the region defined by y2=8x and x=2 (a)…

Q: Evaluate the triple integral. 2xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: 12) Find +he integral of the f(xiyia)=x+y? function on the region between the x4y1 and x?+y"= 9…

A: Convert the integral in cylindrical coordinate: ∭Vfx,y,zdxdydz=∫z=01∬1≤x2+y2≤9x2+y2dxdydz…

Q: Evaluate E=∭D(x2+y2+z2)−3/2dV where D is the region bounded by the surfaces x2+y2+z2=9 and…

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Q: Use Green's Theorem to evaluate the line integral. | (x - 4y) dx + (x + y) dy C: boundary of the…

A: The given integral is ∫Cx-4y dx+ x+y dy,  where C is the region bounded by x2+y2=1 and  x2+y2=16 To…

Q: Evaluate the triple integral. SSSE2.xy dV , where E lies under the plane : = 1+x + y and above the…

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

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Q: and y = 2u, evaluate the integral xy³dA where c) Using the transformation x =-; 6u region R is…

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Q: a)Calculate the integral [D zdV on the D region bounded by the 6 = x2 + y2 paraboloid from the…

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Q: (i) Evaluate the double integral (x + y) dxdy where D is the triangular region in the xy plane with…

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Q: Use Green's Theorem to evaluate the line integral: 2xy dx + 4x² y² dy Where C is the simply…

A: Use formula of Green's theorem to solve this problem.

Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

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

A:

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: Evaluate the triple integral. 3xy dV, where E lies under the plane z = 1 + x + y and above the…

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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: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: Evaluate the triple integral. 2xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Final answer is 65/84.

Q: The area of the region defined by Il æ| – |y|| < 1 and a + y < 1 in the xy plane is a. T b. 27 С. Зт…

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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: 2. For the region D enclosed by y = - x, y = 1 – x, y = x, y = x + 2, use an appropriate…

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Q: Evaluate the triple integral. SSSE 7xy dV¸ where E lies under the plane = 1+x+ y and above the…

A: We have to Evaluate the triple integral.

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 the triple integral ∭E (x+7y)dV where E is bounded by the parabolic cylinder y=2x^2 and the…

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Q: 3. Evaluate the triple integral where E is the region behind y = 10 – 2z and in front of the region…

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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 calculate S,x²y³dx + (xy – y²)dy where C is the boundary of the region lying…

A: Greens Theorem:

Q: 6. Evaluate the triple integral ry dV where E is bounded by the parabolic cylinders y = x² and r =…

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

A: Line integration by using 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: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

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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: 2. Let R be the region in the first quadrant of the xy-plane bounded by the hyperbolas xy = 1, xy =…

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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. 4xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: Evaluate the triple integral. 5xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A: The point of intersection of the cylinder x=y2 and y=x2 is 0 and 1.

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

A: First I have changed the line integral into double integral with the help of Green's theorem and…

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

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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: Use the transformation u = x2 - y? and v = 2xy to evaluate (x2 + y2)dx dy for the R region R bounded…

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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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Q: A. Evaluate and sketch the line integral :1 = f yx dx + (2X – Y)dy around the region bounded by…

A: Greens theorem

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

A: