Inverse Trigo substitution - 1.jpg

There are some standard substitutions, where we put value of x and solve it

Inverse Trigonometry substitution table - teachoo.jpg

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Concept wise

Transcript

Sometimes while integrating, We get questions like โˆซ1โ–’โˆš(๐‘Ž^2โˆ’๐‘ฅ^2 ) ๐‘‘๐‘ฅ Now, how do we solve it? There are some standard substitutions, where we put value of x and solve it โˆš(๐‘Ž^2โˆ’๐‘ฅ^2 ) ๐‘ฅ=๐‘Ž ๐‘ ๐‘–๐‘›โก๐œƒ 1โˆ’ใ€–๐‘ ๐‘–๐‘›ใ€—^2โก๐œƒ=ใ€–๐‘๐‘œ๐‘ ใ€—^2โก๐œƒ โˆš(๐‘Ž^2+๐‘ฅ^2 ) ๐‘ฅ=๐‘Ž ๐‘ก๐‘Ž๐‘›โก๐œƒ 1+ใ€–๐‘ก๐‘Ž๐‘›ใ€—^2โก๐œƒ=ใ€–๐‘ ๐‘’๐‘ใ€—^2โก๐œƒ โˆš(๐‘ฅ^2โˆ’๐‘Ž^2 ) ๐‘ฅ=๐‘Ž ๐‘ ๐‘’๐‘โก๐œƒ ใ€–๐‘ ๐‘’๐‘ใ€—^2โก๐œƒโˆ’1=ใ€–๐‘ก๐‘Ž๐‘›ใ€—^2โก๐œƒ

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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.