Ex 7.4, 2 - Integrate 1 / root 1 + 4x2 - Class 12 NCERT - Ex 7.4

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

Transcript

Ex 7.4, 2(Method 1) 1/โˆš(1 + 4๐‘ฅ^2 ) โˆซ1โ–’1/โˆš(1 + 4๐‘ฅ^2 ) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš(4 (1/4 + ๐‘ฅ^2 ) ) . ๐‘‘๐‘ฅ =โˆซ1โ–’1/(โˆš4 โˆš(1/4 + ๐‘ฅ^2 )) . ๐‘‘๐‘ฅ =1/2 โˆซ1โ–’1/โˆš(๐‘ฅ^2 + 1/4) . ๐‘‘๐‘ฅ =1/2 logโก|๐‘ฅ+โˆš(4๐‘ฅ^2 + 1)/2|+๐ถ =1/2 logโก|(2๐‘ฅ + โˆš(4๐‘ฅ^2 + 1))/2|+๐ถ =1/2 [logโก|2๐‘ฅ + โˆš(1+4๐‘ฅ^2 ) |โˆ’logโก2 ]+๐ถ =1/2 logโก|2๐‘ฅ + โˆš(1+4๐‘ฅ^2 ) |โˆ’1/2 logโก2+๐ถ =๐Ÿ/๐Ÿ ๐’๐’๐’ˆโก|๐Ÿ๐’™ + โˆš(๐Ÿ+๐Ÿ’๐’™^๐Ÿ ) |+๐‘ช

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