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Solved 6) Use a parametrization to express the area of the - Chegg Question: 6) Use a parametrization to express the area of the surface as a double integral Then evaluate the integral (There are many correct ways to set up the integrals) a) Circular cylinder band: The portion of the cylinder x2 + y2 = 1 between the planes z = 1 and z = 4 b) Parabolic cap: The cap cut from the paraboloid z = 2 – x2 - y2 by the cone z = √x² + y² =
Solved Let D be the smaller cap cut from a solid ball of - Chegg Advanced Math questions and answers Let D be the smaller cap cut from a solid ball of radius 18 units by a plane 9 units from the center of the sphere Express the volume of D as an iterated triple integral in (a) spherical, (b) cylindrical, and (c) rectangular coordinates Then (d) find the volume by evaluating one of the three triple integrals
multivariable calculus - Finding the outward flux through a sphere . . . Problem: Find the flux of of the field F F across the portion of the sphere x2 +y2 +z2 =a2 x 2 + y 2 + z 2 = a 2 in the first octant in the direction away from the origin, when F = zxi^ + zyj^ +z2k^ F = z x i ^ + z y j ^ + z 2 k ^
calculus - Spherical Cap Area - Mathematics Stack Exchange Find the Area of the upper Cap cut from the sphere x2 +y2 +z2 = 2 x 2 + y 2 + z 2 = 2 by the cylinder x2 +y2 = 1 x 2 + y 2 = 1 I got how to solve it after seeing solution using dS = ∬ dz dx2 + dz dy2 − 1− −−−−−−−−−−√ dxdy d S = ∬ d z d x 2 + d z d y 2 − 1 d x d y But in my attempt using spherical coordinates I got a different answer (which is wrong) I don't
Parabaloid surface area problem - Mathematics Stack Exchange Find the area of the surface of the cap cut from the paraboloid z = 12 −x2 −y2 z = 12 x 2 y 2 by the cone z =x2 +y2 z = x 2 + y 2 I've seen some approaches of taking the magnitude of the cross product of the two partial derivatives of the equation of the parabaloid, but I still don't know how the equation of the cone plays into this problem