Example 29 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 29 Evaluate β«_((βπ)/4)^(π/4)βsin^2β‘π₯ ππ₯ Let f(x) = γπ ππγ^2 π₯ f(-x) = γπ ππγ^2 (βπ₯)=(βsinβ‘π₯ )^2=γπ ππγ^2 π₯ Since f(x) = f(-x) Hence, γπ ππγ^2 π₯ is an even function β«_((βπ)/4)^(π/4)βsin^2β‘π₯ ππ₯=β«_0^(π/4)βsin^2β‘π₯ ππ₯ = β«_0^(π/4)β((1 β cosβ‘γ2 γ π₯)/2) ππ₯ = 2β«_0^(π/4)βγ[1/2β(cosβ‘2 π₯)/2] ππ₯γ = 2 [π₯/2βsinβ‘2π₯/(2Γ2)]_0^(π/4) = 2 [π₯/2βsinβ‘2π₯/4]_0^(π/4) Putting Limits = 2(π/4 (1/2)βsinβ‘2(π/4)/4) β 2 (0/2βsinβ‘2(0)/4) = 2(π/8 ββ‘γsinβ‘(π/2)/4γ )β0 = 2 (π/8β1/4) = π /πβπ/π
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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