(a) Iff is a piecewise continuous and T-periodic, then show that for a R [f(x) f(x)...

 

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(a) Iff is a piecewise continuous and T-periodic, then show that for a R [f(x) f(x) dr = f(r) dr. dr= Ja You may assume that f is continuous. (5 Marks) (b) Consider a function f: RR, and for a R, define the function F by F (r) = f(r) dr for all r E R. Assume that fis T-periodic (L > 0), show that F is T-periodic if and only if f f (7) dr = 0. (15 Marks) [20 Marks] (a) Iff is a piecewise continuous and T-periodic, then show that for a R [f(x) f(x) dr = f(r) dr. dr= Ja You may assume that f is continuous. (5 Marks) (b) Consider a function f: RR, and for a R, define the function F by F (r) = f(r) dr for all r E R. Assume that fis T-periodic (L > 0), show that F is T-periodic if and only if f f (7) dr = 0. (15 Marks) [20 Marks]