Ex 7.10, 4 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Ex 7.10
Ex 7.10, 1
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Chapter 7 Class 12 Integrals
Serial order wise
Transcript
Ex 7.10, 4 By using the properties of definite integrals, evaluate the integrals : β«_0^(π/2)β(cos^5β‘π₯ ππ₯)/(sin^5β‘π₯ + cos^5β‘π₯ ) Let I=β«_0^(π/2)βγcos^5β‘π₯/(sin^5β‘π₯ + cos^5β‘π₯ ) ππ₯γ I= β«_0^(π/2)βγ(cos^5 (π/2 β π₯))/(γπ ππγ^5 (π/2 β π₯) + γπππ γ^5 (π/2 β π₯) ) ππ₯γ β΄ I = β«_0^(π/2)βγ sin^5β‘π₯/(cos^5β‘π₯ + sin^5β‘π₯ ) ππ₯γ Adding (1) and (2) i.e. (1) + (2) I+I=(γπππ γ^5 π₯)/(γπ ππγ^5 π₯ + γπππ γ^5 π₯) ππ₯+β«_0^(π/2)βγsin^5β‘π₯/(cos^5β‘π₯ + sin^5β‘π₯ ) ππ₯γ 2I=β«_0^(π/2)βγ[(γπππ γ^5 π₯ + γπ ππγ^5 π₯)/(γπππ γ^5 π₯ + γπ ππγ^5 π₯)] ππ₯γ 2I= β«_0^(π/2)βγ ππ₯γ I=1/2 β«_0^(π/2)βγ ππ₯γ I=1/2 [π₯]_0^(π/2) I=1/2 [π/2β0] π°=π /π
