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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

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 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

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.