`f` and `g` be two positive real valued functions defined on `[-1,1]` such that `f(-x)=(1)/(f(x))` and `g` is an even function with `int_(-1)^(1)g(x)dx=1` then `I=int _(-1)^(1) f(x)g(x)dx` satisfies

If int f(x)dx=g(x) then int f^(-1)(x)dx is

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

Let f(x) and g(x) be two continuous functions defined from R rarr R, such that f(x_(1))>f(x_(2)) and g(x_(1)) f(g(3 alpha-4))

Let f and g be two real values functions defined by f(x)=x+1 and g(x)=2x-3 Find 1)f+g,2 ) f-g,3 ) (f)/(g)

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

Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

If a function f(x) satisfies f'(x)=g(x) . Then, the value of int_(a)^(b)f(x)g(x)dx is

If f(x) and g(x) are two continuous functions defined on [-a,a], then the value of int_(-a)^(a){f(x)+f(-x)}{g(x)-g(-x)}dx is