Ex 7.3, 24 - Chapter 7 Class 12 Integrals
Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.3, 24 β«1β(π^π₯ (1 + π₯))/(cos^2β‘(π^π₯ π₯) ) ππ₯ equals (A) βcotβ‘(ππ₯^π₯ ) + πΆ (B) tanβ‘(π₯π^π₯ ) + πΆ (C) tanβ‘(π^π₯) + πΆ (D) cotβ‘(π^π₯) + πΆ β«1β(π^π₯ (1 + π₯))/cos^2β‘(π₯π^π₯ ) ππ₯ Put γπ₯πγ^π₯=π‘ Differentiating w.r.t.x π(π₯)/ππ₯ . π^π₯+π(π^π₯ )/ππ₯ . π₯=ππ‘/ππ₯ π^π₯+(π^π₯ ). π₯=ππ‘/ππ₯ Using product rule as (π’π£)^β²=π’^β² π£+ π£^β² π’ π^π₯ (1+π₯)=ππ‘/ππ₯ ππ₯=ππ‘/(π^π₯ (1 + π₯) ) Thus, our equation becomes β«1β(π^π₯ (1 + π₯))/cos^2β‘(π₯π^π₯ ) ππ₯ = β«1β(π^π₯ (1 + π₯))/cos^2β‘(π‘) Γ ππ‘/(π^π₯ (1 + π₯) ) =β«1βππ‘/cos^2β‘π‘ . ππ‘ =β«1βsec^2β‘π‘ . ππ‘ =tanβ‘π‘+πΆ Putting value of π‘=π₯π^π₯ =tanβ‘(π₯π^π₯ )+πΆ β΄ B is correct answer ( As β«1βsec^2β‘π₯ ππ₯=tanβ‘π₯+πΆ)
Ex 7.3
Ex 7.3, 1
Ex 7.3, 2
Ex 7.3, 3 Important
Ex 7.3, 4 Important
Ex 7.3, 5
Ex 7.3, 6 Important
Ex 7.3, 7
Ex 7.3, 8
Ex 7.3, 9 Important
Ex 7.3, 10 Important
Ex 7.3, 11
Ex 7.3, 12
Ex 7.3, 13
Ex 7.3, 14
Ex 7.3, 15
Ex 7.3, 16 Important
Ex 7.3, 17
Ex 7.3, 18 Important
Ex 7.3, 19 Important
Ex 7.3, 20 Important
Ex 7.3, 21
Ex 7.3, 22 Important
Ex 7.3, 23
Ex 7.3, 24 Important You are here
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.