Ex 7.3, 24 - Chapter 7 Class 12 Integrals
Last updated at May 29, 2018 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‘(ππ₯) + πΆ D. cotβ‘(ππ₯) + 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₯ 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 Hence B is correct answer
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