Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented rectangle, bounded by x = -a , x = a, y = -c and y = c

Q: Let C be the positively oriented square with vertices (0,0), (1,0), (1, 1), (0, 1). Use Green's…

A: Let's solve by using green theorem.

Q: Let C be the positively oriented square with vertices 0, 1, 1 + i, i. Evaluate using the definition…

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Q: Given: ZWZX ZYZX; ZW = ZY Prove: ZX is a perpendicular bisector of WY

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Q: c) By using Green's theorem, evaluate $ (In (x²) + xy² – y²) dx + (ev + x²y – 3xy) dy, where C is…

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Q: Let C be the positively oriented square with vertices (0,0) (2,0), (2,2), (0,2) Use Green's Theorem…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+ x² + y?, the cylinder E x2 + y? = 1, and…

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Q: Use Green's Theorem to evaluate the line integral. (a) | e2a+y dx +e¬Y dy, where C'is the triangle…

A: In the question we have to evaluate integral. NOTE - As per Bartleby's policy we can not solve…

Q: (c) Use Green's Theorem to evaluate (3xydx+ 2xy dy, where C is a counterclockwise oriented…

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Q: If E is the solid shape bounded by x 2 0,y 20 ,z 2 0 and the plane 2x + 3y +z = 6 evaluate (x + y)…

A: The given question is solved below

Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y°, the cylinder z² + y² = 2, and…

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Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy'dy, where C is the triangle with…

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Q: A solid G is bounded by the paraboloid z = 4 - x? – y?, the cylinder x² + y? = 4 and the plane z =…

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Q: a) Evaluate (-ri-yj+2z k) n dS, where a is the portion of the paraboloid : 3x +3y between the planes…

A: We have to Evaluate the Integral using polar coordinate

Q: Let R be the trapezoid with vertices (1,-1), (3,3), (3,-3) and (9,9). Give a change of variables to…

A: Given that ,  R be the trapezoid with vertices (1,-1) , (3,3) ,(3,-3) and (9,9) . Let , the vertices…

Q: Let C be the positively oriented square with vertices 0, 1, 1 + i, i. Evaluate using the definition…

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Q: AXYZ is isosceles with base YZ and M is any point on YZ. Prove that a. ZXMY > ZY Z. b. XM < XY M

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x² + y°, the cylinder 2² + y? = 5, and…

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Q: Use Stoke's theorem to evaluate the integral xydx +x*dy– 4x'ydz where C C is the boundary of the…

A: Given: ∫Cxydx+x2dy-4x3ydzBoundry square surfaces z=1vertices are (1,0,1),(1,1,1) &amp; (0,1,1) &amp;…

Q: | Let C be the positively oriented square with vertices (0, 0), (2, 0), (2, 2). (0, 2). Use Green's…

A: greens theorem

Q: Let C be the positively oriented square with vertices (0, 0), (2,0), (2, 2), (0, 2). Use Green's…

A: Let the given square be OABC which is positively oriented.

Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

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Q: Let M be an elliptic paraboloid a = y? + z². Compute the Gauss map and the shape operator. Find k…

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Q: If F = xy?i + yz? j + zx2k, and S is the region bounded by the triangle with vertices (1,0,0),…

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Q: Use Stokes’ Theorem to evaluate ∫c F ⋅ dr. In each case C is oriented counterclockwise as viewed…

A: Given: f(x,y,z) = xyi + yzj + zxk C is part of paraboloid z= 1- x2-y2   so, A/c to stroke theoram…

Q: Compute where C is the counter dockwise oriented boundary of upper-half unit disc D. a)…

A: We know that from gobern's theoram ∫Qdx +ψdy ⇒∬∂ψ∂x-∂∂ydxdy Now ∮C(y2dx+3xydy) use green's theorem…

Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

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Q: Consider D to be the region below the paraboloid z = 3+x² + y² , inside the cylinder x + y² =1 and…

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Q: Use Green’s Theorem to evaluate the line integral Z C−→F . d−→r , where C is the circle x^2 + y^2 =…

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Q: Let F = < 4x + y², 5y + z, 9z + x So F. dī, Use Stokes' Theorem to evaluate C where C is the…

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Q: Let C be the positively oriented square with vertices (0, 0), (2,0). (2, 2). (0, 2). Use Green's…

A: Green's Theorem:  For a positively oriented curve C∫CP dx+Q dy=∫∫D∂Q∂x-∂P∂y dAfor the region D…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x² + y°, the cylinder 2² + y? 1, and the…

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Q: Calculate F- dS if F(x, y, z) = x²ye²i+ æy?j – 2xye*k, where S is the surface of the box bounded by…

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Q: Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's…

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Q: 11. Let F(r, y) = (ry', yr') and let C be the boundary of unit square: 0 Ss 1, 0< yS1. Use Green's…

A: That's easy. Have a great day!!!

Q: Use Green's Theorem to evaluate x dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+x² + y°, the cylinder x² + y? = 3, and the…

A: Here we have to evaluate ∫∫∫E ez dV , where E is the enclosed by the paraboloid z=4+x2+y2 , the…

Q: let s is the curved surface of the cylinder x²÷a² + y²÷b²=1 0≤z≤c , then evaluate…

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Q: A solid G is bounded by the paraboloid z = 4 – r - y², the cylinder 2+ y = 4 and the plane z = 5.…

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Q: Let E denote the part of the plane x + y + z = 1 that is inside the cylinder r? + y? = 1. Compute…

A: We have to find the value of  ∬ F→.dS→

Q: find ⌠⌠F*dS if F(x,y,z)=2xi+2yj+2zk and S is the paraboloid z=8-x^2-y^2 lying above the rectangle…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 4 + x² + y², the %3D cylinder x? + y² = 3,…

A: We need to evaluate integral.

Q: Calculate ⌠⌠F*dS if F(x,y,z)=x^2ye^zi + xy^2j-2xye^zk where S is the surface of the box bounded by…

A: Use projection on xy plane

Q: Evaluate the line integral Levis where C is the half circle x² + y² = 1, y ≥ 0. x² + y² ds

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Q: $ ((x,y) (E,6) )e product Prove 2 xt + 3yt on e?. Gompute inner IL(,2), where the norm i's…

A: We have to prove that f( (x, y) , (t, t) ) = 2xt + 3yt is an inner product on R2 . 1.) &lt; ( 0, 0 )…

Q: Use Stokes' Theorem to evaluate ∫CF⋅dr where F(x,y,z)=xi+yj+3(x2+y2)k and C is the boundary of the…

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Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…

Q: Evaluate z dv, where E is enclosed by the paraboloid z = x² + y2 and the plane z = 16.

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