# Ex 7.8, 6

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex7.8, 6 0 4 + 2 Let I1 = 0 4 + 2 I1 = 0 4 . + 0 4 2 . Solving I2 I2 = 0 4 . Putting =0 =4 = = 4 0 = 4 & = We can write it as 0 4 . = 4 0 uc1 1 0 + 0+ + 0+2 + + 0+ 1 =4 uc1 1 0 + + 2 + + 1 = 0 =0 0+ =0+ = 0+2 =0+2 =2 0+ 1 =0+ 1 = 1 Thus, 0 4 . = 4 0 uc1 1 0 + 0+ + 0+2 + + 0+ 1 =4 uc1 1 0+ +2 + + 1 =4 uc1 1 1+2+3+ + 1 =4 uc1 1 1 2 =4 uc1 1 2 =4 uc1 1 2 4 =4 uc1 1 4 2 =4 uc1 1 1 2 =4 . 2 uc1 1 1 =8 1 1 uc1 =8 1 0 =8 Solving I3 I3 = 0 4 2 . Putting =0 =4 = = 4 0 = 4 & = 2 We can write it as 0 4 2 . = 4 0 uc1 1 0 + 0+ + 0+2 + + 0+ 1 =4 uc1 1 0 + + 2 + + 1 = 2 0 = 2 . 0 = 0 =1 0+ = 2 0 + = 2 0+2 = 2 0 + 2 = 2 2 . 0+ 1 = 2 0 + 1 = 2 1 0 4 2 . =4 uc1 1 0 + + 2 + + 1 =4 uc1 1 1+ 2 + 2 2 + + 2 1 =4 uc1 1+ 2 + 4 + + 2 1 Let S = 1+ 2 + 4 + + 2 1 It is G.P with common ratio (r) , = 4 2 = 4 2 = 2 We know, Sum of G.P = a 1 1 Replacing a by 1 and r by 2 , we get S = 1 2 1 2 1 = 2 1 2 1 Thus, 0 4 2 . =4 uc1 1+ 2 + 4 + + 2 1 = 4 uc1 1 2 1 2 1 = 4 uc1 1 2 1 2 1 2 1 2 = 4 uc1 2 1 2 uc1 1 2 1 2 Taking uc1 1 2 1 2 As, 4 0 0 2 0 uc1 1 2 1 2 = 2 0 1 2 1 2 = 1 1 = 1 Thus, 0 4 2 . = 4 uc1 2 1 2 uc1 1 2 1 2 = 4 uc1 2 1 2 .1 = 4 uc1 2 4 1 2 4 .1 = 4 uc1 8 1 8 = 4 8 1 8 = 8 1 2 Putting the values of I2 and I3 in I1 I1 = 0 4 . + 0 4 2 . = 8 + 8 1 2 = 16 + 8 1 2 = +

Chapter 7 Class 12 Integrals

Ex 7.1, 10
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Ex 7.1, 18 Important

Ex 7.1, 20 Important

Ex 7.2, 20 Important

Ex 7.2, 26 Important

Ex 7.2, 35 Important

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Ex 7.3, 6 Important

Ex 7.3, 13 Important

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Ex 7.3, 22 Important

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Example 9 Important

Example 10 Important

Ex 7.4, 8 Important

Ex 7.4, 15 Important

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Ex 7.4, 25 Important

Example 15 Important

Ex 7.5, 9 Important

Ex 7.5, 11 Important

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Example 20 Important

Example 22 Important

Ex 7.6, 13 Important

Ex 7.6, 14 Important

Ex 7.6, 18 Important

Ex 7.6, 19 Important

Ex 7.6, 24 Important

Ex 7.7, 5 Important

Ex 7.7, 10 Important

Ex 7.7, 11 Important

Example 25 Important

Ex 7.8, 4 Important

Ex 7.8, 6 Important You are here

Example 27 Important

Ex 7.9, 15 Important

Ex 7.9, 16 Important

Ex 7.9, 20 Important

Ex 7.9, 22 Important

Ex 7.10, 4 Important

Ex 7.10, 7 Important

Ex 7.10, 8 Important

Ex 7.10, 9 Important

Example 30 Important

Example 34 Important

Example 36 Important

Ex 7.11,8 Important

Ex 7.11, 18 Important

Example 40 Important

Example 41 Important

Example 44 Important

Misc 18 Important

Misc 8 Important

Misc 19 Important

Misc 24 Important

Misc 30 Important

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Misc 41 Important

Misc 44 Important

Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.