1.

The value of ..............

Answer»


Solution :`(A)= int_(-pi)^(x) ubrace(cos 2x. cos 2^(2)x. cos 2^(3)x. cos 2^(4) x. cos 2^(5)x)_(f(x))")"dx`
`I=2 int_(0)^(pi) f(x) dx`
[f(x) is EVEN]
`I=2.2 int_(0)^(pi//2) f(x) dx`
`:' f(pi-x) = f(x)`
`I= 4 int_(0)^(pi//2) f(x) dx =4 l_(1)`
Now, `l_(1)= int_(0)^(pi//2) f(x)dx`
`l_(1)=-l_(1)`
`:' f(pi/2 -x)=-f(x)`
`l_(1)=0`
`IMPLIES l=0`


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