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Chapter 7 Class 12 Integrals
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Ex 7.10, 13 By using the properties of definite integrals, evaluate the integrals : ∫_((βˆ’ πœ‹)/2)^(πœ‹/2)β–’sin^7⁑π‘₯ 𝑑π‘₯ This is of form ∫_(βˆ’π‘Ž)^π‘Žβ–’π‘“(π‘₯)𝑑π‘₯ 𝑓(π‘₯)=sin^7⁑π‘₯ 𝑓(βˆ’π‘₯)=sin^7⁑(βˆ’π‘₯)=(βˆ’π‘ π‘–π‘›π‘₯)^7=(βˆ’1)^7 (𝑠𝑖𝑛π‘₯)^7=βˆ’sin^7⁑π‘₯ Thus, 𝑓(βˆ’π‘₯) =βˆ’π‘“β‘(π‘₯) ∴ ∫_((βˆ’πœ‹)/2)^(πœ‹/2)β–’sin^7⁑〖π‘₯ 𝑑π‘₯=πŸŽγ€—

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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.