int_(0)^((pi)/(3))(f(x))/(f(x)+f((pi-3x)/(3)))dx=

int_(0)^((alpha)/3)(f(x))/(f(x)+f((alpha-3x)/3))dx=

int_(0)^((alpha)/3)(f(x))/(f(x)+f((alpha-3x)/3))dx=

int_(0)^(alpha//3)(f(x))/(f(x)+f((alpha-3x)/(3)))dx=

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

If f(x)=(sin x)/(x)AA x in(0,pi], prove that (pi)/(2)int_(0)^((pi)/(2))f(x)f((pi)/(2)-x)dx=int_(0)^( pi)f(x)dx

What is the value of int_0^pi((f(x))/(f(x)+f(pi/2-x)))dx ?

int_(0)^(pi//2)(f(sec x))/(f(sec x)+f(cosec x))dx=

int_((pi)/(5))^((3pi)/(10))(f(sin x))/(f(sin x) + f(cos x)) dx

Match the following {:("List - 1","List - II"),("I) "int_(-1)^(1)x|x|dx,"a) "(pi)/(2)),("II) "int_(0)^((pi)/(2))(1+log((4+3sinx)/(4+3cosx)))dx,"b) "int_(0)^((pi)/(2))f(x)dx),("III) "int_(0)^(a)f(x)dx,"c) "int_(0)^(a)[f(x)+f(-x)]dx),("IV) "int_(-a)^(a)f(x)dx,"d) "0),(,"e) "int_(0)^(a)f(a-x)dx):}