Example

Solution (Upper Sum)

Lower Sum

Mid point Rule

Summary

Sigma Notation

Examples

Example

Algebra Rules for Summation

Some useful Formulae

Riemann Sum

Norm of partition P

Example

Definite Integral

Dummy Variable

Existence of Definite Integral

Rules obeyed by Definite Integrals

Example

Integral as Area Under the Curve

Some tips

Average Value of a Function

Exercise 5.3

27 – 62 - odd

Fundamental Theorem of Calculus (Part – 1)

Fundamental Theorem of Calculus (Part – 2)

Fundamental Theorem of Calculus

Exercise 5.4

37 – 46 - odd

Indefinite Integral and Substitution Rule

The power Rule in Integral Form

Examples

Steps for Substitution Rule

Examples

Using different Substitutions

The integrals of Sin2x and Cos2x

Area under the curve y = Sin2x

Assignment # 5.

Exercise 5.5(1 – 54 odd)

Substitution and Area between Curves

Substitution by two methods

Example

Theorem

Integrating Even Function

Area between intersecting curves

Example

Ex 5.6