The value of the integral [[Fnds, where s is the surface of the cube in bounded by x 0, x = 2, у %3D 0, у 2, z = 0, z = 2 and f = 4xzi- y'j+ yzk, is

Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

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Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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Q: Sketch the cylinder given by x = 4- Z*2（z square）in three-dimensional space.

A: Given: The equation is x=4-z2. To sketch: The given equation in three-dimensional space.

Q: 5. Find the centroid of the area bounded by the curve y = 4- x², the line x = 1 and the coordinate…

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Q: Use Green's Theorem to find the integral rdy - dr where C is the curve consisting of three line…

A: Given integral is: ∫Cxdy-ydx

Q: 5) Consider the parallelogram with vertices (0,0), (4,0), (6,2) & (2, 2). We know the area of this…

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Q: Evaluate exp{}dA where R is the region in the ry-plane bounded by the trapezoid with vertices (0,…

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Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

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Q: Evaluate the line integral, where C is the given space curve. [xerza xez ds, C is the line segment…

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Q: Jse Green's Theorem to evaluate the line integral along the positively oriented closed curve C.…

A: The equation of a straight line joining two points x1, y1 and x2, y2 is given by the formula: y-y1 =…

Q: Find the area of the surface defined by x + y + z = 1, x2 + 2y2 ≤ 1.

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Q: A region R consists of a square bounded by the lines x = -5, x = 5, y = 0, and y = -10 and a half…

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Q: u?i + uvj + v²k bounded by the Find the area of the surface R(u, v) inequalities |u| < 2, \v| < 2.

A: Given that, R(u,v) = u2 i + uv j + v2 k With  We have to use the formula of surface area, Here, Ru…

Q: Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the…

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Q: b) The line integral F. dr is a scalar.

A: Check whether given statement is true or false.

Q: Jo F dr, where F = (3-2y, x-1, -2z) and C is the boundary of a triangle with vertices (0, 0, -3),…

A: Given F=3-2y, x-1, -2z C is the boundary of a triangle with vertices (0, 0, -3), (0, 4, 5), (2, 0,…

Q: Find the centroid of the plane area bounded by the parabola y = 6x - x² and the line y = x

A: To Find: The centroid of the plane area bounded by the parabola y=6x-x2 and the line y=x

Q: Evaluate line integral f,dr where f=(x2+y2)i and c is the rectangle in the xy plane bounded by…

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Q: Let F 8x'i + 8y³j + 8z°k. Evaluate the surface integral of F over the unit sphere.

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