6. ` int_(0)^(a)int_(x)^((a^2)/x) f(x,y)dxdy`

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

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

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

int_(0)^(2)int_(0)^(x)int_(0)^(y)xydxdydz

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

prove that : int_(0)^(2a) f(x)dx = int_(0)^(a) f(x)dx + int_(0)^(a)f(2a-x)dx

int_(-1)^(1)int_(0)^(2)int_(x-2)^(x+2)(x+y+z)dxdydz

If f and g are continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

Prove that: int_(0)^(2a)f(x)dx=int_(0)^(2a)f(2a-x)dx

If fandg are continuous function on [0,a] satisfying f(x)=f(a-x)andg(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx