Integration Type 3

-

Integration Type 3

Formulas

i.         

ii.        

iii.      

iv.       

 

Example1: Evaluate

Solution: we have,

                                        

                                            

                                            

                                            

Example 2: Evaluate

Solution: We have,

                                        

                                        

                                                              

                                                          

                        

                        

Example 3:

Solution: We have

                                        

                                            

                                            

                                            

Example 4: Evaluate

Solution: We have


Comments

Post a Comment

Popular posts from this blog

Chapter 1 : Set Theory: An Introduction

-
Image
Return to Table of Content   Mathematics for Biotechnology and Data Science  Chapter 1: Set Theory  Chapter 2: Operation of Sets  Chapter 3: Application of Set Theory   Chapter 4: Venn Diagram    Chapter 5: Relation    Chapter 6:  MAPPING OR FUNCTIONS   Chapter 8: Inverse of a Function   1]   SETS AND THEIR REPRESENTATION Definition of a Set: A well-defined collection of distinct objects is called Set. Example 1: The collection of vowels in English alphabets. This set containing five elements, namely a,e,i,o,u. Example 2: A collection of favourite singers is not a set because it varies from person to person. If a is an element of a set A, then we write a   A and say a belongs to A or a is in A or a is member of A. If a does not belongs to A, we write a   A. Example 3: ‘a’ belongs to the set of vowels in English alphabets. Example 4: The collection of all states in the Indian union is a set. ...
Read more

Table of content

-
Table of Content  Formulas: Differentiation  Integration: Type 1  Integration: Type 2 Calculus of Several Variables                 1 Functions of two variables               2 Limits of function of two variables              3 Continuity of function of two variables               4 Partial Differentiation Part 1               5 Partial Differentiation Part 2              6 Partial Differentiation Part 3               7 Total derivatives              8 Total derivatives                9 Maxima and minima .  ...
Read more

Chapter 6 : Function or Mapping.

-
Image
Return to Table of Content     Mathematics for Biotechnology and Data Science  Chapter 1: Set Theory  Chapter 2: Operation of Sets  Chapter 3: Application of Set Theory   Chapter 4: Venn Diagram    Chapter 5: Relation    Chapter 6:   MAPPING OR FUNCTIONS   Chapter 8: Inverse of a Function  Chapter 6:  MAPPING OR FUNCTIONS 6.1: Function: A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by   where   is the input. The general representation of a function is . Definitions: 1. Write the definition of a mapping. Let A and B be two non-empty sets. A relation f from A to B, i.e., a subset of , is called a function (or a mapping or a map) from A to B if     I. ...
Read more