Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 7 + x + y?, the cylinder x2 + y? = 7, and the xy-plane. e dv

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: Use spherical coordinates to evaluate /R Vx2 + y² + z² dV , where B is the ball x² + y? + z? < 10 В

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Q: Evaluate the integral, where E is enclosed by the paraboloid z = 9 + x² + y?, the cylinder x2 + y2 =…

A: In cylindrical coordinates:-x=r cos θy=r sin θ z=z Also, x2 +y2 =r2  And, ∫∫∫f(x, y, z)…

Q: 2. Use cylindrical coordinates to evaluate √√9-x² 9-x²-y² [dz x² dz dy dx. √9-x2 0

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Q: Use cylindrical coordinates. Evaluate √x² + y² dv, where E is the region that lies inside the…

A: The region lies inside the region x2+y2=4 and between the planes z=-5 and z=-2. We have to evaluate…

Q: Use spherical coordinates to evaluate the triple integral x² + y² + z² dV, where E is the ball: x² +…

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Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. O x2y dx,…

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Q: :f (x, y, 2) = x + y; E = {(x, y, z) |1 0, y > 0}

A: In this question given that a function and it is in the cartetion coordinate. We can convert in…

Q: 3. (15 pants) Evaluate the line integral Y ds where C is part of the parabola y = x² from (0,0) to…

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Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

A: Solution:

Q: Evaluate the integral by changing to cylindrical coordinates. V 16 - x2 16 - x2 - y2 x² + y? dz dy…

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

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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: Consider the contour represented in the following figure. The points marked on the figure are А(3,…

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Q: (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = U-v, z = 1+2u+v, 0 ≤…

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Q: Evaluate II| 6x(x2 + y2) dv, where E is the solid in the first octant that lies beneath the…

A: Since the integral lies in first octant so 0≤θ≤π/2 and z≥0.  Converting into cylindrical coordinates…