Chapter 7 Class 12 Integrals
Concept wise

Ex 7.10, 13 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by

Ex 7.10, 13 - Using properties of definite integrals sin7 x dx - Ex 7.10

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo