Use Cartesian coordinates to set up the iterated double integral given by III ² av dV D where D is the tetrahedron in the first octant bounded by the plane 2x + 3y + z = 6. Use dV = dy dx dz. Draw the solid D.

Q: Evaluate the surface integral. JS (x+y+z) dS, S is the parallelogram with parametric equations x = u…

A: We find the surface integral.

Q: Evaluate I Jx2 + y2 dV where B is the region lying above the xy-plane, and below cone z = 16 – Vx² +…

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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: Find the centroid of a thin, flat plate covering the region enclosed by the parabola y2 = x and the…

A: Given information:

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

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Q: Use pola

A: Introduction: To convert the rectangular coordinates x,y into the polar coordinates r,θ, we have,…

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

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Q: Determine the element of surface area dS in the special case of the paraboloid of revolution z = x2…

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Q: Evaluate the surface integral. (x + y + z) dS, S is the parallelogram with parametric equations x =…

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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: Determine the area bounded by the conic sections y = x² – 6² and y = 6² – 2². O 576 O 183 O 281 O…

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Q: Use polar coordinates to find the volume of the solid below the paraboloid z=75−3x2−3y2z=75−3x2−3y2…

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Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3