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

Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.2, 38 โซ1โ(ใ10๐ฅใ^9+ใ10ใ^๐ฅ log_๐โก10)/(๐ฅ10+ 10๐ฅ) dx equals (A) 10๐ฅ โ ๐ฅ^10 + ๐ถ (B) 10๐ฅ+๐ฅ^10+๐ถ (C) (10๐ฅ โ ๐ฅ^10 )^(โ1) + ๐ถ (D) logโก(10๐ฅ+๐ฅ10) + ๐ถ Let ๐ฅ10+ 10๐ฅ= ๐ก Differentiating both sides ๐ค.๐.๐ก.๐ฅ ใ10๐ฅใ^(10โ1)+ใ10ใ^๐ฅ ๐๐๐โก10= ๐๐ก/๐๐ฅ ใ10๐ฅใ^9+ใ10ใ^๐ฅ ๐๐๐โก10= ๐๐ก/๐๐ฅ ๐๐ฅ= ๐๐ก/(ใ10๐ฅใ^9 + ใ10ใ^๐ฅ ๐๐๐โก10 ) (Using (๐^๐ฅ )^โฒ=๐^๐ฅ ๐๐๐โก๐) Now, our function becomes โซ1โใ" " (10๐ฅใ9+10ใ^๐ฅ ๐๐๐โก10)/(๐ฅ^10 + ใ10ใ^๐ฅ )ใ . ๐๐ฅ Putting (๐ฅ^10+ ใ10ใ^๐ฅ )=๐ก & ๐๐ฅ=" " ๐๐ก/(ใ10๐ฅใ^9 + ใ10ใ^๐ฅ ๐๐๐โก10 ) = โซ1โใ" " (10๐ฅใ9+10ใ^๐ฅ ๐๐๐โก10)/๐กใ . ๐๐ก/(ใ10๐ฅใ^9+ใ10ใ^๐ฅ ๐๐๐โก10 ) " " = โซ1โใ" " 1/๐กใ.๐๐ก = log |๐ก|+๐ถ = log |ใ10ใ^๐ฅ+ ๐ฅ^10 |+๐ถ = log (ใ10ใ^๐ฅ+ ๐ฅ^10 )+๐ถ โด Option D is correct. (Using ๐ก=ใ10ใ^๐ฅ+๐ฅ^10) (As 10x and x10 are positive)
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