Question

5. \iint_S \frac{1}{r^2} dS where \mathcal{S} is that part of the cylinder x^2 + y^2 = a^2 bounded by the planes z = 0, z = H (H > 0), and r is the distance between the origin and a point on the surface of \mathcal{S}.

Name: 5. (1)/(r^2) dS where 𝒮 is that part of the cylinder x^2 + y^2 = a^2 bounded by the planes z = 0, z = H (H > 0), and r is the distance between the origin and a point on the surface of 𝒮.
Uploaded: 2022-01-17T22:47:53-08:00
Duration: 4 min 26 s
Channel: Shu-Ting Huang
Description: 5. (1)/(r^2) dS where 𝒮 is that part of the cylinder x^2 + y^2 = a^2 bounded by the planes z = 0, z = H (H > 0), and r is the distance between the origin and a point on the surface of 𝒮.

          5. \iint_S \frac{1}{r^2} dS where \mathcal{S} is that part of the cylinder x^2 + y^2 = a^2 bounded by the planes z = 0, z = H (H > 0), and r is the distance between the origin and a point on the surface of \mathcal{S}.

5. (1)/(r^2) dS where 𝒮 is that part of the cylinder x^2 + y^2 = a^2 bounded by the planes z = 0, z = H (H > 0), and r is the distance between the origin and a point on the surface of 𝒮.

Added by Thomas H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shu-Ting Huang

01/17/2022

Step 1

The surface S is part of the cylinder x^2 + y^2 = a^2 bounded by the planes z = 0 and z = H (where H > 0). Since the surface is a cylinder, it extends infinitely in the z-direction. Therefore, the limits of integration for z will be from 0 to H. Show more…

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∬_(S)(1)/(r^(2))dS where S is that part of the cylinder x^(2)+y^(2)=a^(2) bounded by the planes z=0,z= H(H>0), and r is the distance between the origin and a point on the surface of S. 5.dS where is that part of the cylinder x2+y=a2 bounded by the planes z=0,z= HH > 0)and r is the distance between the origin and a point on the surface of