15_5_3 - x 2 a 2 + y 2 b 2 = 1 is given by S = ZZ x 2 a 2 +...

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3. The plane Ax + By + Cz = D has normal n = A i + B j + C k , and so an area element on it is given by dS = | n | | n k | dx dy = A 2 + B 2 + C 2 | C | dx dy . Hence the area S of that part of the plane lying inside the elliptic cylinder
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Unformatted text preview: x 2 a 2 + y 2 b 2 = 1 is given by S = ZZ x 2 a 2 + y 2 b 2 ≤ 1 √ A 2 + B 2 + C 2 | C | dx dy = π ab √ A 2 + B 2 + C 2 | C | sq. units....
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