Q:-Let ₀∫¹ f(x)dx=1 , ₀∫¹xf(x)dx=2 and ₀∫¹x²f(x)dx=4 , then the number of functions y=f(x) for all x belongs to [0,1],such that f(x)>0 and continuous for all x belongs to [0,1] is

A. 0

B. 1

C. 2

D. 8

Grade 12

1 Answers

∫x²f(x)dx can be writen as x²∫f(x)dx-∫2x(∫f(x)dx)dx and complete the question

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Q:-Let 0∫1 f(x)dx=1 , 0∫1 xf(x)dx=2 and 0∫1 x2f(x)dx=4 , then the number of functions y=f(x) for all x belongs to [0,1],such that f(x)>0 and continuous for all x belongs to [0,1] is A. 0 B. 1 C. 2 D. 8