[4] (61 [10] 2. (a) Show that f(x) = x and g(x) = x2 are orthogonal on the interval (-p, p). (b) Consider the definition

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4 61 10 2 A Show That F X X And G X X2 Are Orthogonal On The Interval P P B Consider The Definition 1 (21.27 KiB) Viewed 43 times

[4] (61 [10] 2. (a) Show that f(x) = x and g(x) = x2 are orthogonal on the interval (-p, p). (b) Consider the definition of a Fourier integral for a function f on the interval (-00,00). Reduce the Fourier integral, if (1) f is even and (ii) f is odd. (c) Consider the function f(1) = e** for 3 € (0,00). (0) Calculate the Fourier cosine integral of f. (i) Calculate the Fourier sine integral of f. (iii) Draw the half-range expanded function f in both cases. Total: [20]