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int(0)^(2a)(f(x)dx)/(f(x)+f(2a-x))=a...

`int_(0)^(2a)(f(x)dx)/(f(x)+f(2a-x))=a`

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Prove that the value of the integral, int_(0)^(2a)(f(x))/(f(x)+f(2a-x))dx is equal to a.

The value of int_(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to -

f(x)>0AAx in R and is bounded. If lim_(n->oo)[int_0^a(f(x)dx)/(f(x)+f(a-x))+aint_a^(2a)(f(x)dx)/(f(x)+f(3a-x)) +a^2int_(2a)^(3a)(f(x)dx)/(f(x)+f(5a-x))+...+a^(n-1)int_((n-1)a)^(n a)(f(x)dx)/(f(x)+f[(2n-1)a-x]]] =7//5 (where a<1), then a is equal to

int_(a)^(b)(f(x)dx)/(f(x)+f(a+b-x))=(1)/(2)(b-a)

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

If f is an odd function, then evaluate I=int_(-a)^a(f(sinx)dx)/(f(cosx)+f(sin^2x))

If f is an odd function, then evaluate I=int_(-a)^a(f(sinx)dx)/(f(cosx)+f(sin^2x))

int_(0)^(2a)f(x)dx is equal to -

If f(x)is integrable function in the interval [-a,a] then show that int_(-a)^(a)f(x)dx=int_(0)^(a)[f(x)+f(-x)]dx.

STATEMENT 1: The value of int_0^(2pi)cos^(99)x dx is 0 STATEMENT 2: int_0^(2a)f(x)dx=2int_0^af(x)dx ,if f(2a-x)=f(x) which of the statement is correct?Is statement 2 correct explanation of statement 1?