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



Last updated at Dec. 23, 2019 by Teachoo
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Misc 3 Integrate the function 1/(๐ฅ โ(๐๐ฅ โ ๐ฅ^2 ) ) โซ1โ1/(๐ฅ โ(๐๐ฅ โ ๐ฅ^2 ) ) ๐๐ฅ = โซ1โ1/(๐ฅ โ(๐ฅ^2 (๐/๐ฅ โ 1) ) ) ๐๐ฅ = โซ1โ1/(๐ฅ . ๐ฅโ((๐/๐ฅ โ 1) ) ) ๐๐ฅ = โซ1โ1/(๐ฅ^2 โ((๐/๐ฅ โ 1) ) ) ๐๐ฅ Let ๐/๐ฅ โ1=๐ก Differentiating both sides ๐ค.๐.๐ก.๐ฅ (โ ๐)/๐ฅ^2 โ0 = ๐๐ก/๐๐ฅ (โ ๐)/๐ฅ^2 = ๐๐ก/๐๐ฅ ๐๐ฅ = (โ ๐ฅ^2)/๐ . ๐๐ก Putting the values of (a/xโ1) and dx, we get โซ1โ1/(๐ฅ^2 โ((๐/๐ฅ โ 1) ) ) ๐๐ฅ = โซ1โ1/(๐ฅ^2 โ๐ก ) ๐๐ฅ = โซ1โ1/(๐ฅ^2 โ๐ก )ร(โ๐ฅ^2)/๐ . ๐๐ก = โซ1โ(โ1)/๐ ๐๐ก/โ๐ก = (โ1)/๐ โซ1โ(๐ก)^(โ 1/2) ๐๐ก = (โ1)/๐ [๐ก^((โ1)/2 + 1)/((โ1)/2 + 1)]+๐ถ = (โ1)/๐ [๐ก^(1/2)/(1/2)] + ๐ถ = (โ2)/๐ [โ๐ก] + ๐ถ Putting back t = ๐/๐ฅโ1 = (โ2)/๐ โ(๐/๐ฅ โ1) + ๐ถ = (โ๐)/๐ โ((๐ โ ๐)/๐) + ๐ช
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