
Ex 7.11
Ex 7.11, 2
Ex 7.11, 3 Important
Ex 7.11, 4
Ex 7.11, 5 Important
Ex 7.11, 6
Ex 7.11,7 Important
Ex 7.11,8 Important
Ex 7.11, 9
Ex 7.11, 10 Important
Ex 7.11, 11 Important
Ex 7.11, 12 Important
Ex 7.11, 13
Ex 7.11, 14
Ex 7.11, 15
Ex 7.11, 16 Important
Ex 7.11, 17 You are here
Ex 7.11, 18 Important
Ex 7.11, 19
Ex 7.11, 20 (MCQ) Important
Ex 7.11, 21 (MCQ) Important
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