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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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