Solve the problem.For f, g in C[a, b], set  = .Show that   defines an inner product of C[a, b].

What will be an ideal response?


Answers will vary.
Inner product Axioms 1-3 follow from elementary properties of definite integrals.  
Axiom 4:   = dt ? 0.
The function [f(t)]2 is continuous and nonnegative on [a, b]. If the definite integral of [f(t)]2 is zero, then [f(t)]2 must be identically zero on [a, b]. Thus,  = 0 implies that f is the zero function on 

Mathematics

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