Ex 7.11, 14 - Chapter 7 Class 12 Integrals (Term 2)
Last updated at Dec. 20, 2019 by Teachoo
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
Definite Integration by properties - P6
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