Ex 7.11, 1 - Chapter 7 Class 12 Integrals (Term 2)

Last updated at Dec. 11, 2021 by Teachoo

Transcript

Ex 7.11, 1 By using the properties of definite integrals, evaluate the integrals : ∫_0^(𝜋/2)▒〖cos^2⁡𝑥 𝑑𝑥〗 Let 𝐈=∫_𝟎^(𝝅/𝟐)▒〖〖𝒄𝒐𝒔〗^𝟐⁡𝒙 𝒅𝒙〗 I=∫_𝟎^(𝝅/𝟐)▒〖〖𝐜𝐨𝐬〗^𝟐⁡ (𝝅/𝟐−𝒙)𝒅𝒙〗 I= ∫_𝟎^((𝝅 )/𝟐)▒〖〖𝐬𝐢𝐧〗^𝟐 𝒙〗⁡𝒅𝒙 Using P4 : ∫_0^𝑎▒〖𝑓(𝑥)𝑑𝑥=〗 ∫_0^𝑎▒𝑓(𝑎−𝑥)𝑑𝑥 (As cos (𝜋/2−𝜃)=sin⁡𝜃) …(2) Adding (1) and (2) I+I= ∫_0^(𝜋/2)▒〖cos^2⁡𝑥 𝑑𝑥〗 + ∫_0^((𝜋 )/2)▒〖sin^2 𝑥〗⁡𝑑𝑥 2I= ∫_0^((𝜋 )/2)▒(cos^2⁡〖𝑥+sin^2⁡𝑥 〗 )⁡𝑑𝑥 𝟐𝐈 =∫_𝟎^((𝝅 )/𝟐)▒〖𝟏 .〗⁡𝒅𝒙 2I=[𝑥]_0^(𝜋/2) 2I =𝜋/2−0 2I =𝜋/2 𝐈=𝝅/𝟒

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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