4. Let D be the region in the first octant bounded by the coordinate planes, the plane x + z = 1 and the cylinder x = 1-y². Which of the integrals below are equivalent to the integral [[[√²³ x² + y² + ²² dV ? e D 1-y² I. I ez²+²+² dz dx dy 0 II. 11. LL²+²+² dy de dz 70 pl P√z pl-z e

Q: Apply Green's Theorem to evaluate the integral (4y² dx + 4x² dy), where C is the triangle bounded by…

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Q: Apply Green's Theorem to evaluate the integral $(2y² dx + 2x² dy), where C is the triangle bounded…

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Q: - a) Evaluate (3 – 6xy)dA where D is the region shown below.

A: According to guidelines we can do only first question. We have to find the area of shaded region…

Q: 6- Evaluate the line integral fe F dr, where F = [ry, yz, r2] and C is the boundary of the…

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Q: Evaluate the line integral f3y² dx + z² dy + (16 - x²) dz over the quarter of the circle of radius 4…

A: Kindly refer to Step 2 for the solution.

Q: 24 dA - I 3x – Y when D is the parallelogram bounded by x – 2y = 0, x – 2y = 2, - and Зх — у 3D 1,…

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Q: 1 [2x²y¢&x +xydv) ces (0, 0), (2, 2) ar

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Q: Compute the volume of the solid bounded by the surfaces x2+y2=17y, z=0 and z=√x2+y².

A: The given problem is to find the volume of the solid bounded by the surfaces x2+y2=17y, z=0 and…

Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: D is the region enclosed by the parabolas = 2 -2 2 = y² - 1 and 2 = x = y² + 1.

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Q: The integral (3-x-y)dA on the triangle in the (x,y) plane bounded by the x-a xis and the lines y x…

A: Use graph to evaluate

Q: Evaluate a. 2+√2 b.v2/2 c. 2V 2 d. 2-V 2 [(y - 1) dA where R is the region bounded by y = 1 - 2² and…

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Q: 3. Let D be the region in the first quadrant (x > 0, y > 0) of the xy-plane bounded by the curves y…

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Q: 4. Evaluate and x = 0. X dA, where D is the region in the first quadrant enclosed by y = x², y = 5,…

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Q: Consider the following population table. 1970 1980 1990 2000 2010 2020 State A 11,110,485 11,427,609…

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Q: Find the work done by F = 3xy³i+ 8x²y²j in moving a particle once counterclockwise around the curve…

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Q: 4. Given an example of a change of coordinates z= r(s,t), y = y(s,t) where every region in the st…

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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: Q2. Let D = 2rza, + r cos² pa.. Evaluate (a) $, D. dS (b) S, V. Ddv over the region defined by 0 srs…

A: All are done in cylindrical coordinates

Q: b. [(x² + y²)dA; Ris the region bounded by y = x and y² = 4x. %3D

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Q: Apply Green's Theorem to evaluate the integral. $x4y +x)dx + (y + 5x)dy с C: The circle (x-4)² + (y…

A: ∮C4y+xdx+y+5xdy where C: x-42+y-82=4