Ex 7.11, 20 The value of ∫_((− 𝜋)/2)^(𝜋/2)▒〖(𝑥^3+𝑥 𝑐𝑜𝑠 𝑥+tan^5⁡〖𝑥+1〗 ) 𝑑𝑥〗 (A) 0 (B) 2 (C) 𝜋 (D) 1 ∫_((−𝜋)/2)^(𝜋/2)▒〖 (𝑥^3+𝑥 𝑐𝑜𝑠 𝑥+tan^5⁡〖𝑥+1〗 ) 𝑑𝑥〗 We know that ∫_(−𝑎)^(+𝑎)▒〖𝑓(𝑥) 𝑑𝑥〗={█(0, 𝑖𝑓 𝑓(−𝑥)=−𝑓(𝑥)@&2∫_0^𝑎▒〖𝑓(𝑥) 𝑑𝑥〗, 𝑖𝑓 𝑓(−𝑥)=𝑓(𝑥) )┤ Thus, our equation becomes ∫_((− 𝜋)/2)^(𝜋/2)▒〖(𝑥^3+𝑥 𝑐𝑜𝑠 𝑥+tan^5⁡〖𝑥+1〗 ) 𝑑𝑥〗 = ∫_0^(𝜋/2)▒〖0 𝑑𝑥+∫_0^(𝜋/2)▒〖0 𝑑𝑥+∫_0^(𝜋/2)▒〖0 𝑑𝑥+𝟐∫_𝟎^(𝝅/𝟐)▒𝒅𝒙〗〗〗 = 2∫_0^(𝜋/2)▒𝑑𝑥 = 2 [𝑥]_0^(𝜋/2) = 2(𝜋/2−0) =𝝅 Thus, correct option is C

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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