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

Let f and g be increasing and decreasing functions,respectively,from [0,oo]to[0,oo] Let h(x)=f(g(x)). If h(0)=0, then h(x)-h(1) is always zero (b) always negative always positive (d) strictly increasing 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.

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

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 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

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