Each of q(y), r(y) and s(y) are continuous functions on [0, 6] such that:

q(y) = q(6-y), r(y) = - r(6-y), and: 3*s(y) - 4*s(6-y) = 5

Evaluate:

     6
   ∫q(y)*r(y)*s(y) dy 
    0

I=∫q(y)r(y)s(y)dy[0,6]
Sub y=6-y
I=∫q(6-y)r(6-y)s(6-y)dy[0,6]
I=-1/4∫q(y)r(y)(3s(y)-5)dy[0,6]
I= -3/4∫q(y)r(y)s(y)dy[0,6]+5/4∫q(y)r(y)dy[0,6]
7I/4=5/4∫q(y)r(y)dy[0,6]
=>I=5/7∫q(y)r(y)dy[0,6]=-5/7∫q(y)r(y)dy[0,6] (Sub y=6-y)
=>I=0

The required value is 0.

Posted by Praneeth on 2008-01-22 03:36:06