Question 7 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

Evaluate ∫ ^π/2 _π/2 x ² sin x dx

Evaluate Integral from -π/2 to π/2 - ∫ x^2 sin xdx - CBSE Class 12 Sa

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Question 7 (Choice 2) Evaluate ∫_((−𝜋)/2)^(𝜋/2)▒〖𝑥2 sin⁡〖𝑥 𝑑𝑥〗〗 This is of form ∫_(−𝑎)^𝑎▒𝑓(𝑥)𝑑𝑥 𝑓(𝑥)=𝑥^2 𝑠𝑖𝑛⁡𝑥 𝑓(−𝑥)=(−𝑥)^2 𝑠𝑖𝑛⁡(−𝑥)=𝑥^2 (−sin⁡𝑥 )=−𝑥^2 sin⁡𝑥 Thus, 𝑓(−𝑥) =−𝑓⁡(𝑥) ∴ ∫_((−𝝅)/𝟐)^(𝝅/𝟐)▒〖𝒙𝟐 𝒔𝒊𝒏⁡〖𝒙 𝒅𝒙〗〗=𝟎 Using the Property : ∫_(−𝑎)^𝑎▒〖𝑓(𝑥)𝑑𝑥=0,〗 if f(−𝑥)=−𝑓(𝑥)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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