
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
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
Ex 7.10, 15 You are here
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 June 13, 2023 by Teachoo
Ex 7.10, 15 By using the properties of definite integrals, evaluate the integrals : β«_0^(π/2)β(sinβ‘π₯ β cosβ‘π₯)/(1 + sinβ‘π₯ cosβ‘π₯ ) ππ₯ Let I=β«_0^(π/2)βγsinβ‘γπ₯ β cosβ‘π₯ γ/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) ππ₯γ β΄ I=β«_0^(π/2)βγ(π ππ(π/2 β π₯) β πππ (π/2 β π₯))/(1 + π ππ(π/2 β π₯) πππ (π/2 β π₯) ) ππ₯γ I=β«_0^(π/2)βγ(cosβ‘π₯ β sinβ‘π₯)/( 1 +γ cosγβ‘π₯ sinβ‘γπ₯ γ ) ππ₯γ Adding (1) and (2)i.e. (1) + (2) I+I=β«_0^(π/2)βγ sinβ‘γπ₯ β cosβ‘π₯ γ/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) ππ₯+γ β«_0^(π/2)βγcosβ‘γπ₯ β sinβ‘π₯ γ/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) ππ₯γ 2I=β«_0^(π/2)βγ sinβ‘γπ₯ β cosβ‘γπ₯ +γ cosγβ‘γπ₯ β sinβ‘π₯ γ γ γ/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) γ ππ₯ 2I=β«_0^(π/2)βγ 0/(1 + sinβ‘γπ₯ cosβ‘π₯ γ ) γ ππ₯ 2I=0 β΄ π=π