Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Example 29 Evaluate ∫_((βˆ’πœ‹)/4)^(πœ‹/4)β–’sin^2⁑π‘₯ 𝑑π‘₯ Let f(x) = 〖𝑠𝑖𝑛〗^2 π‘₯ f(-x) = 〖𝑠𝑖𝑛〗^2 (βˆ’π‘₯)=(βˆ’sin⁑π‘₯ )^2=〖𝑠𝑖𝑛〗^2 π‘₯ Since f(x) = f(-x) Hence, 〖𝑠𝑖𝑛〗^2 π‘₯ is an even function ∫_((βˆ’πœ‹)/4)^(πœ‹/4)β–’sin^2⁑π‘₯ 𝑑π‘₯=∫_0^(πœ‹/4)β–’sin^2⁑π‘₯ 𝑑π‘₯ = ∫_0^(πœ‹/4)β–’((1 βˆ’ cos⁑〖2 γ€— π‘₯)/2) 𝑑π‘₯ = 2∫_0^(πœ‹/4)β–’γ€–[1/2βˆ’(cos⁑2 π‘₯)/2] 𝑑π‘₯γ€— = 2 [π‘₯/2βˆ’sin⁑2π‘₯/(2Γ—2)]_0^(πœ‹/4) = 2 [π‘₯/2βˆ’sin⁑2π‘₯/4]_0^(πœ‹/4) Putting Limits = 2(πœ‹/4 (1/2)βˆ’sin⁑2(πœ‹/4)/4) – 2 (0/2βˆ’sin⁑2(0)/4) = 2(πœ‹/8 βˆ’β‘γ€–sin⁑(πœ‹/2)/4γ€— )βˆ’0 = 2 (πœ‹/8βˆ’1/4) = 𝝅/πŸ’βˆ’πŸ/𝟐

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Davneet Singh

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.