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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