Let I = , zdV ,where D is bounded by the planes x = 0, z = 0, x+ y = 2 and the cylinder x2 + z2 = 1 in the first octant, then I = %3D %3D 6.

Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

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Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

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Q: Let r(t) be a positively oriented rectangle with corners (0,0), (0,1), (2,1) and (2,0) and F(r, y)…

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Q: The region W lies between the spheres x² + y² + z² = 4 and x² + y² + z² = 16 and within the cone z =…

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Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

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Q: Let D be the triangular region in the uv-plane with vertices (0, 1), (4, 1), (1, 3) and let G(u, v)…

A: Given :-  Let D be the triangular region in the u-v plane with vertices  0, 1 ,  4 , 1 ,  1, 3. Let…

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A: Using Lagrange multiply method

Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

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Q: Sketch the domain D in the (x, y)-plane satisfying ≤ y ≤ 2e- and e ≤ y ≤ 3e. In your sketch, label D…

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