Unformatted text preview: x2 + x1 = ² x 1 / 2x1 / 2 ³ 2 . (5) This suggests that we can write (3) as a perfect square by simply changing a sign in the righthand side of (5): x + 2 + x1 = ² x 1 / 2 + x1 / 2 ³ 2 . Returning now to (2), the integration can be handled in a straightforward way, L = 1 2 Z 9 1 q ( x 1 / 2 + x1 / 2 ) 2 dx = 1 2 Z 9 1 ² x 1 / 2 + x1 / 2 ³ dx (6) = 1 2 x 3 / 2 3 / 2 + x 1 / 2 1 / 2 !µ µ µ µ µ 9 1 = 32 3 , where the positivity of x has been used in (6)....
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 Fall '10
 KIHYUNHYUN
 Calculus, Perfect square, Square number

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