Let `f(a)>0`, and let `f(x)` be a non-decreasing continuous function in `[a, b]`. Then,`1/(b-a)int_a^bf (x) dx` has the

Let f(a)>0, and let f(x) be a non- decreasing continuous function in [a,b]. Then,(1)/(b-a)int_(a)^(b)f(x)dx has the

Let f(x) be a continuous function and I = int_(1)^(9) sqrt(x)f(x) dx , then

Let f(x),x>=0, be a non-negative continuous function.If f'(x)cos x =0, then find f((5 pi)/(3))

Let f(x) be a continuous periodic function with period T. Let I= int_(a)^(a+T) f(x)dx . Then

Let f(x) and g(x) be any two continuous function in the interval [0, b] and 'a' be any point between 0 and b. Which satisfy the following conditions : f(x)=f(a-x), g(x)+g(a-x)=3, f(a+b-x)=f(x) . Also int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx, int_(a)^(b)f(x)dx=int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx int_(0)^(a)f(x)dx=p" then " int_(0)^(a)f(x)g(x)dx is

Let f(x) and g(x) be any two continuous function in the interval [0, b] and 'a' be any point between 0 and b. Which satisfy the following conditions : f(x)=f(a-x), g(x)+g(a-x)=3, f(a+b-x)=f(x) . Also int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx, int_(a)^(b)f(x)dx=int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx If int_(0)^(a//2)f(x)dx=p," then "int_(0)^(a)f(x)dx is equal to

Let f(x) and g(x) be any two continuous function in the interval [0, b] and 'a' be any point between 0 and b. Which satisfy the following conditions : f(x)=f(a-x), g(x)+g(a-x)=3, f(a+b-x)=f(x) . Also int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx, int_(a)^(b)f(x)dx=int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx If f(a+b-x)=f(x) , then int_(a)^(b)xf(x)dx is

Let f(x),x>=0, be a non-negative continuous function,and let F(x)=int_(0)^(x)f(t)dt,x>=0, if for some c>0,f(x) =0, then show that f(x)=0 for all x>=0.

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for x in [0, a] . Then int_(0)^(a)(dx)/(1+e^(f(x))) is equal to