Integral calculus is used for solving the problems of the following types.
a) the problem of finding a function if its derivative is given.
b) the problem of finding the area bounded by the graph of a function under given conditions. Thus the Integral calculus is divided into two types.
- Definite Integrals (the value of the integrals are definite)
- Indefinite Integrals (the value of the integral is indefinite with an arbitrary constant, C)
Indefinite Integrals
These are the integrals that do not have a pre-existing value of limits; thus making the final value of integral indefinite. ∫g'(x)dx = g(x) + c. Indefinite integrals belong to the family of parallel curves.
Definite Integrals
The definite integrals have a pre-existing value of limits, thus making the final value of an integral, definite. if f(x) is a function of the curve, then
b∫ af(x) dx= f(b)−f(a)
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