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Ex 7.11, 20 - Value of (x3 + x cos x + tan5 x + 1) dx - Ex 7.11

Ex 7.11, 20 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.11, 20 The value of ∫_((βˆ’ πœ‹)/2)^(πœ‹/2)β–’γ€–(π‘₯^3+π‘₯ π‘π‘œπ‘  π‘₯+tan^5⁑〖π‘₯+1γ€— ) 𝑑π‘₯γ€— (A) 0 (B) 2 (C) πœ‹ (D) 1 ∫_((βˆ’πœ‹)/2)^(πœ‹/2)β–’γ€– (π‘₯^3+π‘₯ π‘π‘œπ‘  π‘₯+tan^5⁑〖π‘₯+1γ€— ) 𝑑π‘₯γ€— We know that ∫_(βˆ’π‘Ž)^(+π‘Ž)▒〖𝑓(π‘₯) 𝑑π‘₯γ€—={β–ˆ(0, 𝑖𝑓 𝑓(βˆ’π‘₯)=βˆ’π‘“(π‘₯)@&2∫_0^π‘Žβ–’γ€–π‘“(π‘₯) 𝑑π‘₯γ€—, 𝑖𝑓 𝑓(βˆ’π‘₯)=𝑓(π‘₯) )─ Thus, our equation becomes ∫_((βˆ’ πœ‹)/2)^(πœ‹/2)β–’γ€–(π‘₯^3+π‘₯ π‘π‘œπ‘  π‘₯+tan^5⁑〖π‘₯+1γ€— ) 𝑑π‘₯γ€— = ∫_0^(πœ‹/2)β–’γ€–0 𝑑π‘₯+∫_0^(πœ‹/2)β–’γ€–0 𝑑π‘₯+∫_0^(πœ‹/2)β–’γ€–0 𝑑π‘₯+𝟐∫_𝟎^(𝝅/𝟐)▒𝒅𝒙〗〗〗 = 2∫_0^(πœ‹/2)▒𝑑π‘₯ = 2 [π‘₯]_0^(πœ‹/2) = 2(πœ‹/2βˆ’0) =𝝅 Thus, correct option is C

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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.