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Ex 7.11

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Ex 7.11, 14 You are here

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Ex 7.11, 20 (MCQ) Important

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Chapter 7 Class 12 Integrals

Serial order wise

Last updated at Dec. 20, 2019 by Teachoo

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Ex 7.11, 14 By using the properties of definite integrals, evaluate the integrals : β«_0^2πβcos^5β‘π₯ ππ₯ β«_0^2πβcos^5β‘π₯ ππ₯ =β«_0^πβcos^5β‘π₯ ππ₯+β«_0^πβγcos^5 (2Οβπ₯)γ ππ₯ = β«_0^πβγγπππ γ^5 π₯ ππ₯+β«_0^πβγπππ γ^5 γ π₯ = 2 β«_0^πβγγπππ γ^5 π₯ ππ₯γ Using property: β«_0^2πβγπ(π₯)ππ₯=β«_0^πβγπ(π₯)ππ₯+β«_0^πβπ(2πβπ₯)ππ₯γγ (As cos (2Ο β π) = cos π) Using property: β«_0^2πβγπ(π₯)ππ₯=β«_0^πβγπ(π₯)ππ₯+β«_0^πβπ(2πβπ₯)ππ₯γγ = 2 (β«_0^(π/2)βγγπππ γ^5 π₯ ππ₯+β«_0^(π/2)βγcosβ‘(πβπ₯) γγ ππ₯) = 2 (β«_0^(π/2)βγγπππ γ^5 π₯ ππ₯+β«_0^(π/2)βγ(β cos π₯)^5β‘ππ₯ γγ) = 2 (β«_0^(π/2)βγγπππ γ^5 π₯ ππ₯ββ«_0^(π/2)βγγγπππ γ^5 π₯γβ‘ππ₯ γγ) = 2Γ0 = 0 (cos (πβπ) = β cos π)