If `f(x)=f(4-x), g(x)+g(4-x)=3` and `int_(0)^(4)f(x)dx=2`, then : `int_(0)^(4)f(x)g(x)dx=`

If f(a-x)=f(x) and int_(0)^(a//2)f(x)dx=p , then : int_(0)^(a)f(x)dx=

If f(2-x)=f(2+x),f(4+x)=f(4-x) and int_(0)^(2)f(x)dx=5 then int_(0)^(50)f(x)dx is

If f(x) and g(x) be continuous functions in [0,a] such that f(x)=f(a-x),g(x)+g(a-x)=2 and int_0^a f(x)dx=k , then int_0^a f(x)g(x)dx= (A) 0 (B) k (C) 2k (D) none of these

If (d)/(dx)[g(x)]=f(x) , then : int_(a)^(b)f(x)g(x)dx=

If f(x)+f(pi-x)=1 and g(x)+g(pi-x)=1 , then : int_(0)^(pi)[f(x)+g(x)]dx=

If int_(-1)^(4)f(x)dx=4 and int_(2)^(4)[3-f(x)]dx=7 , then int_(2)^(-1)f(x)dx=

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

If int_(-1) ^(4) f(x) dx=4and int_(2)^(4) (3-f(x))dx=7, then int_(-1) ^(2) f(x) dx=