Let us locale the vertices of the rectangle \vhen a > I.

Chapter 0, Problem 11.6

(choose chapter or problem)

Let us locale the vertices of the rectangle \vhen a > I. As shown in Fig. 183. x1 = -a. X:2 = - I .. q = I. and_,-~ = a. All four vertices can be described in terms of two positive numbers band c lhi.ll depend on lhc value of o in lhc following manner: (I 0) b = /1 lg(x)I dx = ; dx lo o V( I - x:2 )(a:2 - .r:2) ( I J ) c= /"lg(.r)ldx= /" dx 11 ./1 y(x2 - I )(a 2 - x:2) If - I < x < 0. lhen c.u-g(.r +a)= arg(x +I)= 0 and mg(.r - I)= arg(.r - a) = n: hence g(x) = [cxr(- ~i) r lg(xll = -lgC.tll. Ir -a < x < - I. then g(x) = [exp(- ~i) r lg(x >I = il.~lx >I Thus u:1 = - ; "g(X) d.r = - r I g(X) d.r -1 11 g(X) d.r 0 lo . I = { -i lg(.r)I dx - i ; 11 lg(.r)I dx = -b + ic. lo -I h is le fl lo lhe exercises lo show lhal (I 2) u1, = -b. lJI~ = /J + ic. The position and dimensions of the rcclangle arc shown in Fig. 183.