SOLUTION: Let vector space P2 have an inner product defined as ⟨p, q⟩ = ∫[-1 to 1] p(x)q(x) dx Find d(1, x)

Question 1167701: Let vector space P2 have an inner product defined as
⟨p, q⟩ = ∫[-1 to 1] p(x)q(x) dx
Find d(1, x)
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.


Then d(1,x)  is the inner product  


    (1-x,1-x) = integral from -1 to 1 of (1-x)^2 dx,


which is the same as the integral from -1 to 1 of (x-1)^2 dx.


Antiderivative is  ,  and from it, you easily get the answer


     = .

Solved, explained and answered.

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