Example 32 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 32 Evaluate β«_0^(π/2)βsin^4β‘π₯/(sin^4β‘π₯ + cos^4β‘π₯ ) ππ₯ Let I =β«_0^((π )/2)βγ(γπ ππγ^4 π₯)/γγπ ππγ^4 π₯γβ‘γ+ γπππ γ^4 π₯γ ππ₯γ β΄ I =β«_0^((π )/2)βsin^4β‘(π/2 β π₯)/(γγπ ππγ^4 π₯γβ‘γ (π/2 β π₯) γ+ γγπππ γ^4 π₯γβ‘(π/2 β π₯) ) ππ₯ I = β«_0^((π )/2)β(γπππ γ^4 π₯)/γγπππ γ^4 π₯γβ‘γ+γπ ππγ^4 π₯γ ππ₯ Adding (1) and (2) i.e. (1) + (2) I + I = β«_0^((π )/2)β(γπ ππγ^4 π₯)/(γπ ππγ^4 π₯ +γπππ γ^4 π₯) ππ₯+β«_0^(π/2)βγ(πππ π₯)/(γπ ππγ^4 π₯ +γπππ γ^4 π₯).γ ππ₯ 2I = β«_0^((π )/2)βγ(γπ ππγ^4 π₯ + γπππ γ^4 π₯)/(γπ ππγ^4 π₯ +γπππ γ^4 π₯).γ ππ₯ 2I = β«_0^((π )/2)βππ₯" " 2I = [π₯]_0^(π/2) 2I = [π/2β0] I = π/(2 Γ 2) β΄ π = π /π
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About the Author
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