# The value of the integral ∫ 1 { x2 + x2013/(x2 + 2IxI +1)}dx -1 (1) positive (2) negative (3) zero (4) infinite dx is

1
the question is not clear... x2013 ?? what does it mean ? what is the expression in numerator... x square + x2013 or only x2013 ? use parentheses if required to clearly write the expression
it is x to the power 2013 and x square .. & limit of the integration is from 1 to -1 .. please help me

2015-06-18T23:28:10+05:30

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I suppose the given expression inside the integral is as below.

Let f(x) be function inside ONE Integral on the RHS.  Then let X= -x.

In the given integral is anti symmetric function.  so its image wrt y axis.  So  G(x) = - G(-x).  Hence,  the area under the curve G(x) for x > 0 is equal and opposite to the area under the curve for  x < 0.

click on thanks button above please
what is antisymmetric function?
how do u know that G(X) = -G(-X)