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Let f(x) be a continuous, periodic and bounded function with period 3 such that ₀^3 f(t) d t=6 . Also g^ (x)=f(x) , such that g(0)=0 . Find the value of _ x 0 x g ( 1 x ) ,

Correct answer

2

Step-by-step solution

aligned & ₀^x g^ (x) d x= ₀^x f(x) d x & g(x)= ₀^x f(t) d t & _ x 0 x g ( 1 x ) Put x= 1 t & _ t g(t) t & _ t ₀^t f(x) d x t aligned et t=n a where n I a is period =3 _ t ₀^ n a f(t) d t n a = n ₀^3 f(x) d x 3 n = 6 3 =2

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