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15_5_21 - 2 3 2 Let u = r 2 δ 2 du = 2 r dr = 2 π × 1 2...

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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
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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 | ....
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