Integral Calculus – I Bernhard Riemann ( th September - th July ) XII Std - Business Maths & Stat EM Chapter - - Integral Calculus – I Learning Objectives After studying this chapter, the students will be able to understand the indefinite integral. how to find the indefinite integral of a function involving sum, difference and constant multiples. how to use and where to apply the substitution technique in indefinite integrals. the techniques involved in integration by parts and some special type of integrals.
the fundamental theorems of integral calculus. the properties of definite integral and its applications. the application of a particular case of gamma integral. the properties of gamma function.
the evaluation of the definite integral as the limit of a sum. . Indefinite Integrals . .
Concept of Indefinite Integral In differential calculus, we have learned how to calculate the differential coefficient ′ f ( ) of a given function f x ( ) with respect to x . In this chapter, we have to find out the primitive function f x ( ) (i.e. original function) whenever its derived function ′ f ( ) (i.e. derivative of a function) is given, such process is called integration or anti differentiation.
∴ Integration is the reverse process of differentiation We know that d (sin ) cos . Here cos x is known as Derived function , and sin x is known as Primitive function [also called as Anti derivative function (or) Integral function]. Definition . A function F x ( ) is said to be a primitive function of the derived function f x ( ), if d dx F x