15_5_21 - 2 ) 3 / 2 Let u = r 2 + δ 2 du = 2 r dr = 2 π...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
21. The distance from the origin to the plane with equation Ax + By + Cz = D , ( D 6= 0) is δ = | D | A 2 + B 2 + C 2 . If 1 is the plane z = δ , then, since the integrand depends only on distance from the origin, we have ZZ dS ( x 2 + y 2 + z 2 ) 3 / 2 = ZZ 1 dS ( x 2 + y 2 + z 2 ) 3 / 2 = Z 2 π 0 d θ Z 0 r dr ( r 2 + δ
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 ) 3 / 2 Let u = r 2 + δ 2 du = 2 r dr = 2 π × 1 2 Z ∞ δ 2 du u 3 / 2 = π ±-2 √ u ²³ ³ ³ ³ ∞ δ 2 = 2 π δ = 2 π √ A 2 + B 2 + C 2 | D | ....
View Full Document

This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

Ask a homework question - tutors are online