Use spherical coordinate to evaluate V1² + y? + z² dz dy dr.

Q: nter the exact answer. Im z? dz

A: Given, the vertices of the triangle are 0, 2, 2i.

Q: Convert z = 9x2 - 9y2 to cylindrical coordinates.

A: The objective of the question is to convert the given equation in Cartesian coordinates (x, y, z) to…

Q: Sinlxy). lnx dx 19141 to be investipa te the uniform Convergence of ne parametric intepral)

A: Given integral is, ∫01sinxylnxxdx Since, the given integral is improper integral so applying the…

Q: y³ /r² + y² + z²dzdrdy

A:

Q: 8. Set up and evaluate a spherical coordinates integral for the volume of the solid bounded below by…

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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: Evaluate I/| V x2 + y² dV, where E is the region that lies inside the cylinder x2 + y? = 16 and…

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Q: 6. Use spherical coordinates to evaluate SLESE + y² + 2² dzdxdy.

A: The given problem is to evaluate the given triple integral using the spherical coordinates. We have…

Q: 1. Find the volume of the solid determined by x² + y² ≤ ¹ and z¹ ≤ 1.

A: Solution:[1]

Q: 5. Find the volume of the region bounded by the paraboloids z = 12 – x² - y² and z = 2x² + 2y². 2

A: To find volume using triple integral in cylindrical co ordinate system We will use relation between…

Q: 5 25- y² 50-g² –y² Convert (x² + y² + z²)dzdædy into spherical coordinates. ²+y² 5/2 pª cos ødpdød0…

A: Answer:We have to convert∫50∫25-y20∫50-x2-y2x2+y2x2+y2+z2 dzdxdy into sphercal coordinates∵0≤y≤5…

Q: Find the volume of the portion of the ball z² + y² + 2² ≤ 2 that lies above the cone z = √x² + y².…

A: The solution of step 1 is.

Q: Evaluate by changing to spherical coordinates: /2–x²-y² xydzdydx x²+y2

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Q: Q 2/ Sketch and shows the relationship between the Cartesian and Spherical coordinate Pt Te B

A: Solution

Q: B. Identify the center and radius of the ff: x² + y² + 8x + 24 +18 = 0 x² + y² - 6x 12 y = 0 x² + y²…

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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…

Q: 4. Find the volume of the region bounded below by the cone z = 2√x² + y² and above by the sphere x²…

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Q: Evaluate z dv, where E is enclosed by the paraboloid z = x² + y2 and the plane z = 16.

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