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Ex 7.7, 2 - Integrate root 1 - 4x2 - Chapter 7 Integrals - Integration by specific formulaes - Formula 8

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex7.7, 2 (Method 1) โˆš(1โˆ’4๐‘ฅ2) โˆซ1โ–’ใ€–โˆš(1โˆ’4๐‘ฅ^2 ).๐‘‘๐‘ฅใ€— =โˆซ1โ–’ใ€–โˆš(4(1/4โˆ’๐‘ฅ^2 ) ).๐‘‘๐‘ฅใ€— =โˆซ1โ–’ใ€–โˆš4 โˆš(1/4โˆ’๐‘ฅ^2 ).๐‘‘๐‘ฅใ€— =2โˆซ1โ–’ใ€–โˆš((1/2)^2โˆ’๐‘ฅ^2 ).๐‘‘๐‘ฅ" " ใ€— =2[1/2 ๐‘ฅโˆš((1/2)^2โˆ’๐‘ฅ^2 ) +(1/2)^2.1/2 ๐‘ ๐‘–๐‘›^(โˆ’1) ๐‘ฅ/(1/2)+๐ถ1] =2[1/2 ๐‘ฅโˆš(1/4โˆ’๐‘ฅ^2 ) +1/4 . 1/2 ๐‘ ๐‘–๐‘›^(โˆ’1) 2๐‘ฅ+๐ถ1] =2 . 1/2 ๐‘ฅ โˆš(1/4โˆ’๐‘ฅ^2 ) +2 . 1/4 . 1/2 ๐‘ ๐‘–๐‘›^(โˆ’1) 2๐‘ฅ+2๐ถ1 =๐‘ฅโˆš(1/4โˆ’๐‘ฅ^2 )+1/4 ๐‘ ๐‘–๐‘›^(โˆ’1) 2๐‘ฅ+๐ถ =1/4 ๐‘ ๐‘–๐‘›^(โˆ’1) 2๐‘ฅ+๐‘ฅโˆš((1 โˆ’ 4๐‘ฅ^2)/4)++๐ถ =๐Ÿ/๐Ÿ’ ๐’”๐’Š๐’^(โˆ’๐Ÿ) ๐Ÿ๐’™+๐Ÿ/๐Ÿ ๐’™โˆš(๐Ÿ โˆ’ ๐Ÿ’๐’™^๐Ÿ )++๐‘ช =๐‘ก/4 โˆš(1โˆ’๐‘ก^2 )+1/4 ๐‘ ๐‘–๐‘›^(โˆ’1) (๐‘ก)+๐ถ =2๐‘ฅ/4 โˆš(1โˆ’(2๐‘ฅ)^2 )+1/4 ๐‘ ๐‘–๐‘›^(โˆ’1) 2๐‘ฅ+๐ถ =๐Ÿ/๐Ÿ’ ๐’”๐’Š๐’^(โˆ’๐Ÿ) ๐Ÿ๐’™+๐’™/๐Ÿ โˆš(๐Ÿโˆ’๐Ÿ’๐’™^๐Ÿ )+๐‘ช

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