`int_(-a)^(a)f(x)dx=0,` when `f(x)` is an.................function

int_(0)^(a)[f(x)+f(a-x)]dx=

int_(-a)^(a)f(x)dx= 2int_(0)^(a)f(x)dx, if f is an even function 0, if f is an odd function.

int_(0)^(a) (f(a+x) + f(a-x) ) dx =

Prove that : int_(-a)^(a)f(x)dx =2 int_(a)^(0) f(x)dx, if f(x) is even funtion =0 , if f(x) is off fuction.

Prove that int_-a^a f(x) dx=0 , where 'f' is an odd function. And, evaluate, int_-1^1 log[(2-x)/(2+x)] dx

int_(0)^(a)(f(x))/(f(x)+f(a-x))dx=

Property 9: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=0 if f(x) is odd and 2int_(0)^(a)f(x)dx if f(x) is even

STATEMENT 1:int_(a)^(x)f(t)dt is an even function if f(x) is an odd function.STATEMENT 2:int_(a)^(x)f(t)dx is an odd function if f(x) is an even function.

Statement l If f satisfies f(x+y)=f(x)+f(y), AA x,y in R,then int_(-5) ^5 f(x)dx=0 Statement II: If f is an odd function, then int_(-a) ^a f(x) dx =0