Area function : Integral \(\int ^b_a \) f(x) dx represent the area of the region bounded by the curve y = f(x), the ordinate x = a and x = b and x-axis.
Let x be a given point [a, b]. Then \(\int ^b_a \) f(x) dx represent the area of the shaded region A(x).
Clearly, f(x) > 0 ∀ x ∈ [a, b]
The area of shaded region depends upon the value of x.
In other words the area of shaded region is a function of x. If A(x) represent the area of shaded region, then
A(x) = \(\int ^b_a \) f(x) dx
Two basic fundamental theorems have been given here which are based on the area of shadéd region. The parts of these theorems are beyond the scope of this book.
