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If f is a continuous function such that f takes only non-negative values for all xbelongs to R and limit -2 to 2 integration of f(x)dx = 0 , then f(2) equals..:

If f is a continuous function such that f takes only non-negative values for all xbelongs to R and limit -2 to 2 integration of f(x)dx = 0 , then f(2) equals..:

Grade:11

1 Answers

Saurabh Gupta
34 Points
7 years ago

Let I = ∫2-2 f(x) dx = 0,

=> f(x) is an odd function, i.e. f(-x) = -f(x)

 

Thus,

I = f(2) - f(-2) = 0

But, f(-x) = -f(x)

=> I = f(2) -[-f(2)] = 0

=> I = f(2) + f(2) = 0

=> 2f(2) = 0

=> f(2) = 0

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