4. Ris the planar region whose area can be evaluated by: L,(x+ v2 – x) dx + S 2V2 – x dx. -

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

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Q: 10. (1 – y³) dx + (x³ + e*) dy, Č is the boundary of the region between the circles x² + y² = 4 and…

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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: 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: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

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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: Q:A: Determine the area of bounded by y = e, and y = xv +1 at x-axis. y=zv+1

A: Given areas y=e-x2  &amp;  y=x2 +1xand  xasisso required area =∫-30 e-x2 dx + ∫-30  x2+1x dx…

Q: Evaluate || 5x cos y'dxdy where S is the region bounded by y = 2 and 1 x and the y-axis. 4 y =

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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: 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: (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: 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: 4.) evalnate the integral dx aresinx a. WI-Y b) S x arctanx dx

A: We have to solve

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: (1- y*)dx + (x° + e*)dy where C is the boundary of the region between the circles x² + y² = 4 and x²…

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Q: 1. Sketch the region and evaluate the following integral |1. (VI++1)dydx 72 y 4 2 ++++++++H 3 -1 1 4…

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Q: 4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's…

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Q: Evaluate the multiple integral.* 22y [ ✓²)¢ dx dy 10 17.5 16.5 The area hounded by the graphs of y=

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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: 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: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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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: 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: Find the value(s) of c such that the area of the region bounded by the parabolae y=x^2 - c^2 and…

A: Given: The given parabolas are y=x2-c2 and y=c2-x2. Determine the points of intersection.…

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: Evaluate the double integral 4.x dydr 9 + y2 I when A is the shaded region in enclosed by the graphs…

A: Evaluate the double integral.

Q: 1. If R is the region in the first quadrant bounded by x-axis, 3x + y = 6 and y evaluate 3x, Jf 3y…

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Q: 3. Evaluate ff Vr² + y²dA, where R is the region bounded by the circles with center R (0,0) and…

A: Given integral is: ∫∫Rx2+y2dA Where R is the region bounded by the circles with center 0,0 and…

Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

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Q: 4. Evaluate fl, cos (2) dA where D is the region bounded by D = {(x, y)/ vLT <x < V3Ln,0 <y< x² }.

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Q: D be the region that consists of points (x, y) such that x² + (y - 3)² ≤9. Then, (x² + y²) dA equals…

A: see my solution

Q: 18 Evaluate EUE z(x2 +y? +z?) dV where E is the region described by 2 0szs v1-x -y

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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 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: Evaluate SI, cos (2) dA ,where D is the region bounded by (x, y) D = {- sxs V24 ,0 < y< x²} V8n

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Q: SSR (r + y)2 dA, where R is the region bounded by the limaçon r = 2 + cos 0

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Q: The value of the double integral // (2x²y + 9y') d A, D where D is the region bounded by x and y = 2…

A: Given problem:-

Q: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

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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: dV, where E is the region between two cylinders ²+², 5. Evaluate the integral and 2² +2²9 with 1 ≤ y…

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Q: Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.

A: Write the equation of circle into standard form. The radius of the circle is 1.

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: SS Q2: Evaluate (2x + y²) dA where R is the region in the R first octant bounded by circles x² + y²…

A: Introduction: When in a double integral, there is a region that is enclosed by circles, and it is…

Q: O R is the region bounded by x² + y – 4 = 0 and x – y +2 = 0 an is revolved about y = 0.

A: We use washers method to find the integral of that evaluate the volume of the solid of revolution.

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

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Q: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

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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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