Ex 7.10, 11 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by

Ex 7.10, 11 - Evaluate definite integral sin2 x dx - Ex 7.10 - Ex 7.10

part 2 - Ex 7.10, 11 - Ex 7.10 - Serial order wise - Chapter 7 Class 12 Integrals

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Ex 7.10, 11 By using the properties of definite integrals, evaluate the integrals : ∫_((βˆ’ πœ‹)/2)^(πœ‹/2)β–’γ€– sin^2〗⁑π‘₯ 𝑑π‘₯ This is of form ∫_(βˆ’π‘Ž)^π‘Žβ–’π‘“(π‘₯)𝑑π‘₯ where 𝑓(π‘₯)=sin^2⁑π‘₯ 𝑓(βˆ’π‘₯)=sin^2⁑(βˆ’π‘₯)=(βˆ’π‘ π‘–π‘›π‘₯)^2=sin^2⁑π‘₯ ∴ 𝑓(π‘₯)=𝑓(βˆ’π‘₯) ∴ ∫_((βˆ’πœ‹)/2)^(πœ‹/2)β–’γ€–sin^2⁑〖π‘₯ 𝑑π‘₯γ€—=2∫_0^(πœ‹/2)β–’γ€–γ€–π’”π’Šπ’γ€—^𝟐 𝒙 𝑑π‘₯γ€—γ€— =2∫_0^(πœ‹/2)β–’[(𝟏 βˆ’ π’„π’π’”β‘πŸπ’™)/𝟐]𝑑π‘₯ =∫_0^(πœ‹/2)β–’γ€–(1βˆ’cos⁑2π‘₯ ) 𝑑π‘₯γ€— = [π‘₯ βˆ’sin⁑2π‘₯/2]_0^(πœ‹/2) = [πœ‹/2βˆ’sin⁑2(πœ‹/2)/2]βˆ’ [0βˆ’sin⁑〖2(0)γ€—/2] = πœ‹/2βˆ’sinβ‘πœ‹/2βˆ’0 = πœ‹/2βˆ’0+0 = 𝝅/𝟐

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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