Express the integral f(x, y, z) dv as an iterated integral in six different ways, where E is the solid bounded by the given surfaces. y= x², z=0, y + z = 16 /16-4z f(x, y, z) dz dy dx f(x, y, z) dz dx dy f(x, y, z) dx dz dy f(x, y, z) dx dy dz f(x, y, z) dy dz dx f(x, y, z) dy dx dz

Q: Use cylindrical coordinates to calculate the integral of the function f(x, y, z) = z over the region…

A: Given: fx, y, z=z We have to calculate the integral of the given function over the region above the…

Q: Verify Green theorem for the line integral f (x³ -x²y) dx + xy² dy 6x where C is the boundary of the…

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Q: Calculate :/ F. ds, where F (x, y, z) = (-6x³ + 2yz)i + (-6y³ + sin¯¹ (3xz)) j+ (2z+cos (3x²y²)) k…

A: Given F(x,y,z)=-6x3+2yzi^+-6y3+sin-13xzj^+2z+cos3x2y2k^ and S is the outward-oriented surface of the…

Q: c) Use Green's theorem to evaluate the line integral . x2y2 dx + 4x dy, where C is the boundary of…

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Q: For F(x, y, z) = x²z² i+ sinx z²j+zx²y*k, find div F and curl F.

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Q: Find div(curl F) = V. (V x F). F(x, y, z)= xyzi + yj + zk

A: If vector field then from the question

Q: Draw the surfaces z = f(x, y) = x2 + y2 and z = g(x, y) = 8 − x2 − y2 and calculate the volume of…

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Q: c) Use Green's theorem to evaluate the line integral §. x²y² dx + 4x dy, where C is the boundary of…

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Q: Suppose the temperature at a point (x, y, z) of a solid D bounded by the coordinates planes and…

A: Let's find average temperature over the solid.

Q: Evaluate the line integral faF · dr, where F(x, y, z) = -2xi – 5yj + 5zk and C is given by the…

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Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = xz siny-√3 At point (1,1,2).…

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Q: Calculate the line integral fe F. dr, where F = (ry, r? + y? + 22, yz), and C is the boundary of the…

A: Step:-1 Given that a parallelogram with vertices 0, 0, 1, 0, 1, 0, 2, 0, -1, 2, 1, -2 and F→=xy,…

Q: The line integral x dy – y dx Jc x2 + y? is independent of path.

A: Given integral is ∫Cxdy-ydxx2+y2.

Q: Let R be the region in the ry-plane such that /| f(z, y) dA = |(2, y) dy de + | f(x,y) dy dx, (x-2)2…

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Q: Integrate the function f(x, y, z) = (x2 + y2 + z2)4 over the part of the solid cone y2 + z2 ≤ x2…

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Q: Evaluate the line integral [F.dr where Y F(x, y, z) = (x + yz, x + z, xy) and y: line segment from…

A: The given problem is evaluate the given line integral of given vector field F over the given path of…

Q: /|F . d5 where Calculate F = (3zy°, ze", 2ª) Sis the surface of the solid bounded by the cylinder y?…

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