The density at any point is proportional to the distance between the point and the z-axis.

Q: EXAMPLE 5 Find the center of mass of a solid of constant density that is bounded by the parabolic…

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Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: Let B be the ball with center at the origin and radius 1 SS $3(x² + y? + z²)dV = B

A: Solve integral by using Cylindrical cordinates

Q: The disc S is the intersection of the massive sphere x2+ y2+ z2≤2 and the plane x = y. (a) Use…

A: here we need to use spherical coordinate to solve this question.

Q: nd the flux of the vector v=⟨x,y,z⟩ along the surface of the right tetrahedron below.

A: Flux of the vector

Q: Evaluate ∫W z dV, where W is the first-octant portion of the solid sphere of radius 2 centered at…

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Q: Find a parametrization and the equation associated with the cylindrical surface whose directrix and…

A: answer is in step 2

Q: For which value of k is the function 2( – cos(3x))² 1+3x f(x) = k continuous at x = 4. 113 113 113…

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Q: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: Express the point (x, y, z) = (-2, 2, 2/2) in spherical coordinates.

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Q: Use spherical coordinates to find the volume of the top half of the sphere x2+y2+z2 = 4 that lies…

A: The required volume is given by triple integral is  ∫∫∫Rdv     …..(1) where E is the region on the…

Q: .Estimate vu in cylindrical form, in the orthogonal curvilinear coordinates

A: Given: We consider elliptic in cylindrical form .

Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

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Q: A triangle-shaped sheet has a surface mass density of 1.5 grams per square centimeter. Suppose that…

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