" If "f(a+b-x)=f(x)," then "int_(a)^(b)x*f(x)dx=......

If f(a+b-x)=f(x)," then "int_(a)^(b)xf(x)dx=

int_(a)^(b) f(x) dx =

If f(a+b-x) = f(x), then int_a^b xf(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 If f(a+b-x)=f(x) , then int_(a)^(b)xf(x)dx is

If f(a+b-x)=f(x), then prove that int_(a)^(b)xf(x)dx=(a+b)/(2)int_(a)^(b)f(x)dx

int_(a)^(b)f(x)dx=F(b)-F(a) .

If f(a+b-x)=f(x),\ then prove that \ int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx

If f(a+b-x)=f(x),\ then prove that \ int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx

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