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Ex 7.11
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Ex 7.11, 20 (MCQ) Important
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Last updated at March 16, 2023 by Teachoo
Ex 7.11, 17 By using the properties of definite integrals, evaluate the integrals : β«_0^πββπ₯/(βπ₯ + β(π β π₯)) ππ₯ Let I=β«_0^πββπ₯/(βπ₯ + β(π β π₯)) ππ₯ β΄ I=β«_0^πβγβ(π β π₯)/(β(π β π₯) +β(π β (π β π₯) )) ππ₯γ I= β«_0^πβγβ(π β π₯)/(β(π β π₯) + β(π β π + π₯)) ππ₯γ I=β«_0^πβγβ(π β π₯)/(β(π β π₯) + βπ₯) ππ₯γ Adding (1) and (2) i.e (1) + (2) I + I = β«_0^πβγβπ₯/(βπ₯ +β(π β π₯)) ππ₯γ+β«_0^πβγβ(π β π₯)/(β(πβ π₯) + β( π₯)) ππ₯γ 2I = β«_0^πβγ(βπ₯ + β(π β π₯))/(βπ₯ + β(π β π₯)) ππ₯γ 2I =β«_0^πβγ1.ππ₯γ 2I = [π₯]_0^π 2I = [πβ0] π =π/π