Ex 7.10, 1 - Chapter 7 Class 12 Integrals

Last updated at May 29, 2023 by Teachoo

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Ex 7.10, 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

Next: Ex 7.10, 2 → Ask a doubt

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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