NCERT Solutions for Class 12 maths Chapter 7 Integrals


Integration is the inverse process of differentiation. In the differential calculus, we are given a function, and we have to find the derivative or differential of this function. Still, in the integral calculus, we are to find a function whose differential is given. Thus, integration is a process which is the inverse of differentiation. From the geometric point of view, an indefinite integral is collection of the family of curves, each of which is obtained by translating one of the curves parallel to itself upwards or downwards along the y-axis. Integrals, we shall see the definition of indefinite integral, integration as an inverse process of differentiation, geometrical interpretation of indefinite integral, properties of indefinite integral, comparison between differentiation and integration. Methods of integration such as integration by substitution, integration using partial fractions, integration by parts, integration using trigonometric identities, integration of some integral functions, definition and meaning of definite integrals, definite integral as the limit of a sum, fundamental theorem of calculus, evaluation of definite integrals by substitution, some properties of definite integrals and various examples.