int_(a)^(b)f(a+b-x)dx=int_(a)^(b)f(x)d

Using int_(a)^(b)f(a+b-x)dx=int_(a)^(b)f(x) prove the following :

int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx. Hence evaluate : int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx.

If |int_(a)^(b)f(x)dx|=int_(a)^(b)|f(x)|dx,a

Property 4: If f(x) is a comtinuous function on [a;b] then int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

Prove that int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-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

STATEMENT-1 : int_(0)^(2)[x+[x+[x]]]dx=3 and STATEMENT-2 : int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

STATEMENT-1 : int_(0)^(2)[x+[x+[x]]]dx=3 and STATEMENT-2 : int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx