Ex 7.9, 5 - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Definite Integration - By Substitution
Definite Integration - By Substitution
Last updated at April 16, 2024 by Teachoo
Ex 7.9, 5 Evaluate the integrals using substitution β«_0^(π/2 )βsinβ‘π₯/(1 + cos^2β‘π₯ )β‘γ ππ₯γ β«_0^(π/2 )βsinβ‘π₯/(1 + cos^2β‘π₯ )β‘γ ππ₯γ Put cos π₯=π‘ Differentiating w.r.t.π₯ βsinβ‘π₯=ππ‘/ππ₯ ππ₯=(βππ‘)/sinβ‘π₯ Hence when π₯ varies from 0 to π/2, π‘ varies from 1 to 0 Therefore, we can write β«_0^(π/2)βsinβ‘π₯/(1+γ cos^2γβ‘π₯ ) ππ₯=β«_1^0βγsinβ‘π₯/(1 + π‘^2 ) ((βππ‘)/sinβ‘π₯ ) γ =ββ«_1^0βππ‘/(1 + π‘^2 ) =β[tan^(β1)β‘π‘ ]_1^0 =β[tan^(β1)β‘γ(0)βtan^(β1)β‘(1) γ ] =β[0βπ/4] =β[βπ/4] =π /π