Example 32 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Examples
Example 1 (i)
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Chapter 7 Class 12 Integrals
Serial order wise
Transcript
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
