Integration Full Chapter Explained - Integration Class 12 - Everything you need

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Ex 7.2, 39 โˆซ1โ–’๐‘‘๐‘ฅ/(๐‘ ๐‘–๐‘›2 ๐‘ฅ ๐‘๐‘œ๐‘ 2 ๐‘ฅ) equals tan x + cot x + C (B) tan x โ€“ cot x + C (C) tan x cot x + C (D) tan x โ€“ cot 2x + C โˆซ1โ–’ใ€–" " ๐‘‘๐‘ฅ/(sin^2 ๐‘ฅ cos^2โก๐‘ฅ )ใ€— = โˆซ1โ–’ใ€–" " ๐Ÿ/(sin^2 ๐‘ฅ cos^2โก๐‘ฅ ) . ๐‘‘๐‘ฅใ€— = โˆซ1โ–’ใ€–" " (ใ€–๐ฌ๐ข๐งใ€—^๐Ÿ ๐’™ +ใ€– ใ€–๐œ๐จ๐ฌใ€—^๐Ÿใ€—โก๐’™)/(sin^2 ๐‘ฅ cos^2โก๐‘ฅ ) . ๐‘‘๐‘ฅใ€— = โˆซ1โ–’ใ€–" " (sin^2 ๐‘ฅ)/(sin^2 ๐‘ฅ cos^2โก๐‘ฅ ) . ๐‘‘๐‘ฅใ€— + โˆซ1โ–’ใ€–" " ใ€– cos^2ใ€—โก๐‘ฅ/(sin^2 ๐‘ฅ cos^2โก๐‘ฅ ) . ๐‘‘๐‘ฅใ€— = โˆซ1โ–’ใ€–" " 1/cos^2โก๐‘ฅ . ๐‘‘๐‘ฅใ€— + โˆซ1โ–’ใ€–1/(sin^2 ๐‘ฅ) . ๐‘‘๐‘ฅใ€— (Using sin^2โก๐‘ฅ+cos^2โก๐‘ฅ=1) = โˆซ1โ–’ใ€–sec^2โก๐‘ฅ. ๐‘‘๐‘ฅใ€— + โˆซ1โ–’ใ€–๐‘๐‘œ๐‘ ๐‘’๐‘^2 ๐‘ฅ . ๐‘‘๐‘ฅใ€— = ๐’•๐’‚๐’โก๐’™โˆ’๐’„๐’๐’•โก๐’™+๐‘ช โˆด Option B is correct. Using โˆซ1โ–’ใ€–ใ€–๐‘ ๐‘’๐‘ใ€—^2โก๐‘ฅ. ๐‘‘๐‘ฅใ€—=๐‘ก๐‘Ž๐‘›โก๐‘ฅ and โˆซ1โ–’ใ€–๐‘๐‘œ๐‘ ๐‘’๐‘^2 ๐‘ฅ . ๐‘‘๐‘ฅใ€—=โˆ’๐‘๐‘œ๐‘กโก๐‘ฅ

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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.