Integral Calculus

SYLLABUS- INTEGRAL CALCULUS, Paper II: Integral Calculus
Definite Integrals: Integral as a limit of sum, Properties of Definite integrals,
Fundamental theorem of integral calculus, Summation of series by integration, Infinite
integrals, Differentiation and integration under the integral sign.
Functions Defined by Infinite Integrals: Beta function, Properties and various forms,
Gamma function, Recurrence formula and other relations, Relation between Beta and
Gamma function, Evaluation of integrals using Beta and Gamma functions.
Multiple Integrals: Double integrals, Repeated integrals, Evaluation of Double integrals,
Double integral in polar coordinates, Change of variables and Introduction to Jacobians,
Change of order of integration in Double integrals, Triple integrals, Evaluation of Triple
integrals, Drichlet’s theorem and its Liovelle’s extension.
Geometrical Applications of Definite Integrals: Area bounded by curves (quadrature),
Rectification (length of curves), Volumes and Surfaces of Solids of revolution.