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

Last updated at Dec. 20, 2019 by Teachoo

Transcript

Ex 7.11, 20 The value of โซ_((โ ๐)/2)^(๐/2)โใ(๐ฅ^3+๐ฅ ๐๐๐ ๐ฅ+tan^5โกใ๐ฅ+1ใ ) ๐๐ฅใ (A) 0 (B) 2 (C) ๐ (D) 1 โซ_((โ๐)/2)^(๐/2)โใ (๐ฅ^3+๐ฅ ๐๐๐ ๐ฅ+tan^5โกใ๐ฅ+1ใ ) ๐๐ฅใ We know that โซ_(โ๐)^(+๐)โใ๐(๐ฅ) ๐๐ฅใ={โ(0, ๐๐ ๐(โ๐ฅ)=โ๐(๐ฅ)@&2โซ_0^๐โใ๐(๐ฅ) ๐๐ฅใ, ๐๐ ๐(โ๐ฅ)=๐(๐ฅ) )โค Thus, our equation becomes โซ_((โ ๐)/2)^(๐/2)โใ(๐ฅ^3+๐ฅ ๐๐๐ ๐ฅ+tan^5โกใ๐ฅ+1ใ ) ๐๐ฅใ = โซ_0^(๐/2)โใ0 ๐๐ฅ+โซ_0^(๐/2)โใ0 ๐๐ฅ+โซ_0^(๐/2)โใ0 ๐๐ฅ+๐โซ_๐^(๐ /๐)โ๐ ๐ใใใ = 2โซ_0^(๐/2)โ๐๐ฅ = 2 [๐ฅ]_0^(๐/2) = 2(๐/2โ0) =๐ Thus, correct option is C

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