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If f (x+y) =f (x) f(y) for all x,y and ...

If `f (x+y) =f (x) f(y)` for all x,y and `f (0) ne 0, and F (x) =(f(x))/(1+(f (x))^(2))` then:

A

`int _(-2010) ^(2011) F (x)dx =int _(0) ^(2011) F (x)dx `

B

`int _(-2010) ^(2011) F (x)dx =int _(0) ^(2011) F (x)dx =int _(0)^(2011)F (x) dx`

C

`int _(-2010) ^(2011) F (x) dx =0`

D

`int _(-2010) ^(2010) (2F(-x) -F(x)) dx =e int _(0)^(2010) F (x) dx `

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The correct Answer is:
B, D
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VIKAS GUPTA (BLACK BOOK) ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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