Integral Calculus Lecture1 Integration Dated 27 07 2020

Integral Calculus Lecture-1 Integration Dated: -27. 07. 2020 PPT-23 UG (B. Sc. , Part-2) Dr. Md. Ataur Rahman Guest Faculty Department of Mathematics M. L. Arya, College, Kasba PURNEA UNIVERSITY, PURNIA

Contents 1. Definition of integration 2. Indefinite integral 3. Rules of integration 4. Methods of integration 5. Integration of some special functions 6. Definite integral 7. Improper integral 8. Integration as the limit of a sum 9. Reduction formulae 10. Application of integration

Integration (Anti-differentiation) Definition (1): -Integration is the inverse process of differentiation. i. e. Integral or Primitive or anti. Integrand or derivative of f(x) differential coefficient (2) The process of finding the integral (antiderivative) whose derivative is given is called integration.

Indefinite integral We know that i. e. Integrals of cosx are Sinx and Sinx +C Here Sinx is called particular integral and Sinx+C is called general integral (called indefinite integral) Note: - Indefinite integral contains an arbitrary constant C, is called constant of integration

Rules of Indefinite integral Rule I: - If u is a function of x, then where k is a constant. Examples Rule II: Where u, v, w, are functions of x. Examples

Rules of Indefinite integral Rule III: where k is a constant. Example Again,

Methods of integration 1. 2. 3. 4. Method of transformation Method of substitution Integration by parts Integration by partial fraction

Method of transformation Type I Algebraic functions: Express the given function (expression) as the sum or difference following forms by using the formulae of Algebra Tricks: -

Problems Integrate the following w. r. t. Soln (1): -

Solution (4): - Solution (5): -