If `g(1)=g(2),` then `int_(1)^(2)[f{g(x)}]^(-1)f'{g(x)}g'(x)dx` is equal to

If f and g are continuous functions in [0, 1] satisfying f(x) = f(a-x) and g(x) + g(a-x) = a , then int_(0)^(a)f(x)* g(x)dx is equal to

If f and g are continuous functions on [ 0, pi] satisfying f(x) +f(pi-x) =1=g (x)+g(pi-x) then int_(0)^(pi) [f(x)+g(x)] dx is equal to

int x{f(x)^(2) g''(x^(2))-f''(x^(2)) g(x^(2))} dx is equal to

The value of int_1^2 {f(g(x))}^(-1)f'(g(x))g'(x) dx , where g(1)=g(2), is equal to

The value of int_1^2 {f(g(x))}^(-1)f'(g(x))g'(x) dx , where g(1)=g(2), is equal to

int{f(x)g'(x)-f'g(x)}dx equals

If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

If f and g are continuous functions on [0,pi] satisfying f(x)+f(pi-x)=g(x)+g(pi-x)=1 then int_(0)^( pi)[f(x)+g(x)]backslash dx is equal to