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


Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.11, 14 By using the properties of definite integrals, evaluate the integrals : โซ_0^2๐โcos^5โก๐ฅ ๐๐ฅ โซ_0^2๐โcos^5โก๐ฅ ๐๐ฅ =โซ_0^๐โcos^5โก๐ฅ ๐๐ฅ+โซ_0^๐โใcos^5 (2ฯโ๐ฅ)ใ ๐๐ฅ = โซ_0^๐โใใ๐๐๐ ใ^5 ๐ฅ ๐๐ฅ+โซ_0^๐โใ๐๐๐ ใ^5 ใ ๐ฅ = 2 โซ_0^๐โใใ๐๐๐ ใ^5 ๐ฅ ๐๐ฅใ Using property: โซ_0^2๐โใ๐(๐ฅ)๐๐ฅ=โซ_0^๐โใ๐(๐ฅ)๐๐ฅ+โซ_0^๐โ๐(2๐โ๐ฅ)๐๐ฅใใ (As cos (2ฯ โ ๐) = cos ๐) Using property: โซ_0^2๐โใ๐(๐ฅ)๐๐ฅ=โซ_0^๐โใ๐(๐ฅ)๐๐ฅ+โซ_0^๐โ๐(2๐โ๐ฅ)๐๐ฅใใ = 2 (โซ_0^(๐/2)โใใ๐๐๐ ใ^5 ๐ฅ ๐๐ฅ+โซ_0^(๐/2)โใcosโก(๐โ๐ฅ) ใใ ๐๐ฅ) = 2 (โซ_0^(๐/2)โใใ๐๐๐ ใ^5 ๐ฅ ๐๐ฅ+โซ_0^(๐/2)โใ(โ cos ๐ฅ)^5โก๐๐ฅ ใใ) = 2 (โซ_0^(๐/2)โใใ๐๐๐ ใ^5 ๐ฅ ๐๐ฅโโซ_0^(๐/2)โใใใ๐๐๐ ใ^5 ๐ฅใโก๐๐ฅ ใใ) = 2ร0 = 0 (cos (๐โ๐) = โ cos ๐)
Definite Integration by properties - P6
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