15_3_18 - Z ds x 2 + y 2 = Z 1 ds x 2 + y 2 = Z ∞-∞ dx...

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18. The straight line with equation Ax + By = C , ( C 6= 0 ) , lies at distance D = | C | / A 2 + B 2 from the origin. So does the line 1 with equation y = D . Since x 2 + y 2 depends only on distance from the origin, we have, by symmetry,
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Unformatted text preview: Z ds x 2 + y 2 = Z 1 ds x 2 + y 2 = Z ∞-∞ dx x 2 + D 2 = 2 D tan-1 x D ± ± ± ± ∞ = 2 D ² π 2-³ = π D = π √ A 2 + B 2 | C | ....
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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.

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