If a`f(x)`+b`f((1)/(x))=(1)/(x)-5,x ne 0,a ne b`, then `overset(2)underset(1)int f(x)dx` equals

If f(x)=f(a+b-x) , then overset(b)underset(a)int xf(x)dx is equal to

If (d)/(dx)f(x)=g(x) for a le x le b then, overset(b)underset(a)int f(x) g(x) dx equals

The value of the integral overset(2a)underset(0)int (f(x))/(f(x)+f(2a-x))dx is equal to

If f(x)={{:(x,xlt1),(x-1,xge1):} , then underset(0)overset(2)intx^(2)f(x) dx is equal to :

If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b, then f(2) is equal to

If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b, then f(2) is equal to

Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)),(x ne 0) then f(x) equals

If f(x)= {{:(,(1)/(x)-(2)/(e^(2x)-1),x ne 0),(,1,x=0):}

Let overset(a)underset(0)int f(x)dx=lambda and overset(a)underset(0)int f(2a-x)dx=mu . Then, overset(2a)underset(0)int f(x) dx equal to

If f(x)-3f((1)/(x))=2x+3(x ne 0) then f(3) is equal to