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Ex 7.10
Ex 7.10, 2
Ex 7.10, 3 Important
Ex 7.10, 4
Ex 7.10, 5 Important
Ex 7.10, 6
Ex 7.10,7 Important
Ex 7.10,8 Important
Ex 7.10, 9
Ex 7.10, 10 Important
Ex 7.10, 11 Important
Ex 7.10, 12 Important
Ex 7.10, 13
Ex 7.10, 14 You are here
Ex 7.10, 15
Ex 7.10, 16 Important
Ex 7.10, 17
Ex 7.10, 18 Important
Ex 7.10, 19
Ex 7.10, 20 (MCQ) Important
Ex 7.10, 21 (MCQ) Important
Last updated at May 29, 2023 by Teachoo
Ex 7.10, 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)