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Ex 7.2, 39 - Integration dx / sin^2 x cos^2 x equals (A) tan x + cot

Ex 7.2, 39 - Chapter 7 Class 12 Integrals - Part 2

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.