Georg Friedrich Bernhard Riemann (Nineteenth century) was an inspiring German
mathematician. He was very much recognised for his contribution in calculus.
Calculus divides naturally into two parts, namely (i) differential
calculus and (ii) integral calculus. Differential calculus deals with the
derivatives of a function whereas, integral calculus deals with the anti
derivative of the derived function that is, finding a function when its rate of
changemarginal function is known. So integration is the technique to find the
original function from the derived function, the function obtained is called
the indefinite integral. Definite integral is the evaluation of the indefinite
integral between the specified limits, and is equal to the area bounded by the
graph of the function (curve) between the specified limits and the axis. The
area under the curve is approximately equal to the area obtained by summing the
area of the number of inscribed rectangles and the approximation becomes exact
in the limit that the number of rectangles approaches infinity. Therefore both
differential and integral calculus are based on the theory of limits.
The word ‘integrate’ literally means that ‘to find the sum’. So,
we believe that the name “Integral Calculus” has its origin from this process
of summation. Calculus is the mathematical tool used to test theories about the
origins of the universe, the development of tornadoes and hurricanes. It is
also used to find the surplus of consumer and producer, identifying the
probability density function of a continuous random variable, obtain an
original function from its marginal function and etc., in business
In this chapter, we will study about the concept of integral and
some types of method of indefinite and definite integrals.