Integrals are actually of two types. They are definite integral and indefinite integral. In RD Sharma Solutions for Class 12th Maths Chapter 19, indefinite integrals, students study the definition of primitive or anti-derivative and indefinite integral. In this chapter, students study indefinite integrals. An indefinite integral is nothing but an integral which does not have any upper or lower limit. So mathematically, if F (x) is any anti-derivative of f (x), then the most general anti-derivative of f (x) is called an indefinite integral and denoted as,
f x dx=F x+C
Students are taught the fundamental integration formulae and some standard results on integration along with the corollary. Apart from that, they also learn about the integration of trigonometric functions and exponential functions. Along with this, they also practice some miscellaneous problems.
Additionally, students learn about geometrical interpretation of indefinite integral and a major topic that involves the comparison between differentiation and integration. The following are the methods of integration. They are integration by substitution, integration by parts, integration using trigonometric identities, Integration of some particular function and Integral by a partial fraction.
Integration by substitution is discussed in this chapter in a deep manner. Some standard results are also being discussed. And then get a chance to learn topics called evaluation of integrals by using trigonometric substitution and some special integrals. Integration by parts is being taught to the students, along with some important integrals and theorems.
More importantly, integrating rational algebraic functions by using partial functions when the denominator is expressible as a product of distinct linear factors when the denominator contains some repeating linear factors. The various methods for the integration using partial fractions are also taught to the students