Slide5.JPG

Slide6.JPG

  1. Chapter 7 Class 12 Integrals
  2. Concept wise

Transcript

Ex 7.2, 3 Integrate the function: 1/(๐‘ฅ + ๐‘ฅ logโก๐‘ฅ ) 1/(๐‘ฅ + ๐‘ฅ logโก๐‘ฅ )=1/๐‘ฅ(1 + logโก๐‘ฅ ) Step 1: Let 1+logโก๐‘ฅ=๐‘ก Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ 0 + 1/๐‘ฅ=๐‘‘๐‘ก/๐‘‘๐‘ฅ 1/๐‘ฅ=๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=๐‘ฅ ๐‘‘๐‘ก Step 2: Integrating function โˆซ1โ–’1/(๐‘ฅ + ๐‘ฅ logโก๐‘ฅ ) .๐‘‘๐‘ฅ =โˆซ1โ–’1/(๐‘ฅ (1 + logโก๐‘ฅ ) ) .๐‘‘๐‘ฅ" " Putting 1+logโก๐‘ฅ & ๐‘‘๐‘ฅ=๐‘ฅ ๐‘‘๐‘ก = โˆซ1โ–’1/(๐‘ฅ(๐‘ก)) ๐‘‘๐‘ก.๐‘ฅ = โˆซ1โ–’1/๐‘ก ๐‘‘๐‘ก = ๐‘™๐‘œ๐‘”|๐‘ก|+๐ถ Putting back ๐‘ก =1+๐‘™๐‘œ๐‘”โก๐‘ฅ = ๐’๐’๐’ˆ|๐Ÿ+๐ฅ๐จ๐ โก๐’™ |+๐‘ช (๐‘ˆ๐‘ ๐‘–๐‘›๐‘”โˆซ1โ–’ใ€–1/๐‘ฅ ๐‘‘๐‘ฅใ€—=logโก|๐‘ฅ|+๐ถ)

Chapter 7 Class 12 Integrals
Concept wise

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.