1. Chapter 7 Class 12 Integrals
  2. Serial order wise
  3. Ex 7.8
Check sibling questions

Ex 7.8, 15 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by Teachoo

 

Transcript

Ex 7.8, 15 โˆซ_0^1โ–’ใ€–๐‘ฅ๐‘’^(๐‘ฅ^2 ) ใ€— ๐‘‘๐‘ฅ Step 1 :- Let F(๐‘ฅ)=โˆซ1โ–’ใ€–๐‘ฅ๐‘’^(๐‘ฅ^2 ) ๐‘‘๐‘ฅใ€— Let ๐‘ฅ^2=๐‘ก Differentiating w.r.t. ๐‘ฅ 2๐‘ฅ=๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=๐‘‘๐‘ก/2๐‘ฅ Therefore, โˆซ1โ–’ใ€–๐‘ฅ ๐‘’^(๐‘ฅ^2 ) ๐‘‘๐‘ฅ=โˆซ1โ–’ใ€–๐‘ฅ ๐‘’^๐‘ก ๐‘‘๐‘ก/2๐‘ฅใ€—ใ€— =1/2 โˆซ1โ–’ใ€–๐‘’^๐‘ก ๐‘‘๐‘กใ€— =1/2 ๐‘’^๐‘ก Putting ๐‘ก=๐‘ฅ^2 =1/2 ๐‘’^(๐‘ฅ^2 ) Hence, F(๐‘ฅ)=1/2 ๐‘’^(๐‘ฅ^2 ) Step 2 :- โˆซ_0^1โ–’ใ€–๐‘ฅ๐‘’^(๐‘ฅ^2 ) ๐‘‘๐‘ฅใ€—=๐น(1)โˆ’๐น(0) =1/2 ๐‘’^(1^2 )โˆ’1/2 ๐‘’^(0^2 ) =1/2 ๐‘’^1โˆ’1/2 ๐‘’^0 =๐Ÿ/๐Ÿ (๐’†โˆ’๐Ÿ)
  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

    3. Ex 7.8

    Ex 7.9 →
Ex 7.9 →
Chapter 7 Class 12 Integrals
Serial order wise

About the Author

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo