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


Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.1, 22 If ๐/๐๐ฅ f(x) = 4x3 โ 3/๐ฅ4 such that f(2) = 0, then f(x) is x4 + 1/๐ฅ3 โ 129/8 (B) x3 + 1/๐ฅ4 + 129/8 (C) x4 + 1/๐ฅ3 + 129/8 (D) x3 + 1/๐ฅ4 โ 129/8 Given ๐/๐๐ฅ f(x) = 4x3 โ 3/๐ฅ4 Integrating both sides โซ1โใ๐/๐๐ฅ ๐(๐ฅ) ใ=โซ1โ(4๐ฅ^3โ 3/๐ฅ^4 )๐๐ฅ โซ1โ๐/๐๐ฅ ๐(๐ฅ)=4โซ1โใ๐ฅ^3 ๐๐ฅใโ3โซ1โใ1/๐ฅ^4 ๐๐ฅใ ๐(๐ฅ)=4โซ1โใ๐ฅ^3 ๐๐ฅใโ3โซ1โใ๐ฅ^(โ4) ๐๐ฅใ ๐(๐ฅ)=4 ๐ฅ^(3 + 1)/(3 + 1)โ3 ๐ฅ^(โ4 + 1)/(โ4 + 1)+๐ถ ๐(๐ฅ)=4 ๐ฅ^4/4 โ 3 ๐ฅ^(โ3)/(โ3)+๐ถ ๐(๐ฅ)=๐ฅ^4+๐ฅ^(โ3)+๐ถ ๐(๐ฅ)=๐ฅ^4+ 1/๐ฅ^3 +๐ถ Given ๐(2)=0 Putting ๐ฅ=2 in (1) ๐(2)=(2)^4+ 1/(2)^3 +๐ถ 0=16+ 1/8 +๐ถ 0= (128 + 1)/8 +๐ถ 0= 129/8 +๐ถ ๐ถ=(โ129)/8 Putting ๐ถ=(โ129)/8 in (1) ๐(๐ฅ)=๐ฅ^4+ 1/๐ฅ^3 +๐ถ โ ๐(๐)=๐^๐+ ๐/๐^๐ โ๐๐๐/๐ โด Option (A) is correct.
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