Suppose a function fx is continuous and monotonically increa

Suppose a function f(x) is continuous and monotonically increasing on the interval [a,b] with F(x) as the integral of f(x). Find an expression for the equation of the horizontal line that divides the area bounded by the function and the domain and range intervals into two equal parts.

Solution

f(x) is increasing means f(a) < f(x) < f(b) and derivative of f(x) > 0 for all x.

F(x) = integral f(x) dx

Area is nothing but F(x). Because area is integral of f(x) which is equal to F(x).

Area bounnded by function is = b-a

So, equation is x = (b-a)