Area as definite integral:
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Let f (x) be a continuous function in (a, b). Then the area bounded by curve y = f (x),
x axis and lines x = a and x = b can be given by formula
 ,
provided f (x) ≥ 0 (or f(x) ≤ 0) ∀ x ∈ (a , b)
It is at times convenient to use the formula for area with respect to y that is regarding x as a function of y.
The area between x = f(y), y axis and lines
y = c and y = d can be given by
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If we have 2 functions f(x) and g(x) such that f(x) ≤ g(x) ∀ x ∈ [a, b], then the area which is bounded by curves y = f(x), y = g(x) and lines x = a,
x = b (a < b) is given by
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