The function `f` and `g` are positive and continuous. If `f` is increasing and `g` is decreasing, then `int_0^1f(x)[g(x)-g(1-x)]dx`
(a)is always non-positive
(b)is always non-negative
(c)can take positive and negative values
(d)none of these

The function f and g are positive and continuous. If f is increasing and g is decreasing, then int_0^1f(x)[g(x)-g(1-x)]dx is always non-positive is always non-negative can take positive and negative values none of these

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

Let fa n dg be increasing and decreasing functions, respectively, from [0,oo]to[0,oo]dot Let h(x)=f(g(x))dot If h(0)=0, then h(x)-h(1) is (a)always zero (b) always negative always positive (d) strictly increasing none of these

If f and g are two continuous functions being even and and odd, respectively, then int_(-a)^(a)(f(x))/(b^(g(x)+1))dx is equal to (a being any non-zero number and b is positive real number, b ne 1 )

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

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

if f(x) and g(x) are continuous functions, fog is identity function, g'(b) = 5 and g(b) = a then f'(a) is

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

Prove that int_(0)^(a)f(x)g(a-x)dx=int_(0)^(a)g(x)f(a-x)dx .

If f\ a n d\ g are continuious on [0,\ a] and satisfy f(x)=f(a-x)a n d\ g(x)+g(a-x)=2. show that int_0^af(x)g(x)dx=int_0^af(x)dx