If `f(x)a n dg(x)` are continuous functions, then `int_(1nlambda)^(1n1/lambda)(f((x^2)/4)[f(x)-f(-x)])/(g((x^2)/4)[g(x)+g(-x)])dx` is
(a)dependent on `lambda` (b) a none-zero constant (c)zero (d) none of these

int [f(x)g"(x) - f"(x)g(x)]dx is

Evaluate : int_(-(pi)/(2))^((pi)/(2))[f(x)+f(-x)][g(x)-g(-x)]dx

If alpha,beta(beta>alpha), are the roots of g(x)=a x^2+b x+c=0 and f(x) is an even function, then int_alpha^betae^(f((g(x))/(x-alpha)))/(e^(f((g(x))/(x-alpha)))+e^(f((g(x))/(x-beta))))= (a) |b/(2a)| (b) (sqrt(b^2-4a c))/(|2a|) (c) |b/a| (d) none of these

Let f: R to R and g: R to R be continuous function. Then the value of the integral int_(-pi/2)^(pi/2)[f(x)+f(-x)][g(x)-g(-x)]dxi s (a) pi (b) 1 (c) -1 (d) 0

If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n dg(x)+g(a-x)=2, then show that int_0^af(x)g(x)dx=int_0^af(x)dxdot

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

If f(x)=x+tanx and g(x) is the inverse of f(x), then differentiation of g(x) is (a) 1/(1+[g(x)-x]^2) (b) 1/(2-[g(x)+x]^2) (c) 1/(2+[g(x)-x]^2) (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 (a)is always non-positive (b)is always non-negative (c)can take positive and negative values (d)none of these

Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x) .

If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the value of (d)/(dx)((g(x))/(g(g(x)))) at x = 4 equals