Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = E : 6y² + 6z² and x = 6.

Q: 2. Find the surface area of the part of the paraboloid z = x² + y² lying inside the cylinder x² +…

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Q: 2. Sketch the cylinder y = x² +1.

A: complete graph provided below with python code Explanation:  code behind above :  import numpy as…

Q: Integrate f(x, y, z) = 6rz over the region in the first octant (x, y, z 20) above the parabolic…

A: Given that f(x,y,z)=6xz . Which can be expressed as f(x,y,z)=6xz=620  (20xz) . And we will find the…

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z= −y² + x² +4 and above the…

A: The hyperbolic paraboloid is: z=-y2+x2+4. To Do:We have to find the volume under the given…

Q: Evaluate /|/. x dV where E is the solid enclosed by the paraboloid x = y²+z² and the plane x = 9

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Q: Compute the line integral: y² dx + x² dy two ways. C

A: We have an line integralTo evaluate the line integral by two methods (a) By  Green theorem(b) By,…

Q: Find the surface area of the portion of 4x + 3y + 5z = 8 that lies inside the cylinder x² + y² = 49.

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Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: Find the area of the surface. T'part of the paraboloid x = y² + z² that lies inside the cylinder y²…

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Q: Use cylindrical coordinates to evaluate the triple integral √² + y²dV, where E' is the solid bounded…

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Q: Evaluate the triple integral z dV, where E is enclosed by the paraboloid z= 4x2 + 4y2 and the plane…

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Q: Evaluate the triple integral J20² S 2x²z + 2y²z dv where S is the solid that lies below paraboloid z…

A: Given integral: Where  is the solid that lies below paraboloid  and above plane

Q: Calculate the line integral f (2x²y + 10x + 6y − 6) dx + (−6xy + 7) dy, - where C' is the rectangle…

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Q: ce the triple integral

A: Given,          x=9y2+9z2, and x=9

Q: Use Green's Theorem to evaluate the following integral Let² dx + (9x + 5) dy Where C is the triangle…

A: We have to evaluate  where is the triangle with vertices  and .

Q: Calculate the line integral f (−x²y − 3x + 6y + 7) dx + (7xy + 1) dy, where C' is the rectangle with…

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