Evaluate ∫ ^{ π/2 } _{ π/2 } x ^{ 2 } sin x dx
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CBSE Class 12 Sample Paper for 2021 Boards
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CBSE Class 12 Sample Paper for 2021 Boards
Last updated at May 29, 2023 by Teachoo
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
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 𝑠𝑖𝑛𝑥 𝑓(−𝑥)=(−𝑥)^2 𝑠𝑖𝑛(−𝑥)=𝑥^2 (−sin𝑥 )=−𝑥^2 sin𝑥 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)