Ex 7.3, 24 - Integration ex (1 + x) / cos2 (ex x) dx equals - Integration using trigo identities - sin^2,cos^2 etc formulae

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  1. Class 12
  2. Important Question for exams Class 12

Transcript

Ex 7.3, 24 ∫1β–’(𝑒^π‘₯ (1 + π‘₯))/(cos^2⁑(𝑒^π‘₯ π‘₯) ) 𝑑π‘₯ equals A. βˆ’cot⁑(𝑒π‘₯^π‘₯ ) + 𝐢 B. tan⁑(π‘₯𝑒^π‘₯ ) + 𝐢 C. tan⁑(𝑒π‘₯) + 𝐢 D. cot⁑(𝑒π‘₯) + 𝐢 ∫1β–’(𝑒^π‘₯ (1 + π‘₯))/cos^2⁑(π‘₯𝑒^π‘₯ ) 𝑑π‘₯ Put γ€–π‘₯𝑒〗^π‘₯=𝑑 Differentiating w.r.t.x 𝑑(π‘₯)/𝑑π‘₯ . 𝑒^π‘₯+𝑑(𝑒^π‘₯ )/𝑑π‘₯ . π‘₯=𝑑𝑑/𝑑π‘₯ 𝑒^π‘₯+(𝑒^π‘₯ ). π‘₯=𝑑𝑑/𝑑π‘₯ 𝑒^π‘₯ (1+π‘₯)=𝑑𝑑/𝑑π‘₯ 𝑑π‘₯=𝑑𝑑/(𝑒^π‘₯ (1 + π‘₯) ) Thus, our equation becomes ∫1β–’(𝑒^π‘₯ (1 + π‘₯))/cos^2⁑(π‘₯𝑒^π‘₯ ) 𝑑π‘₯ = ∫1β–’(𝑒^π‘₯ (1 + π‘₯))/cos^2⁑(𝑑) Γ— 𝑑𝑑/(𝑒^π‘₯ (1 + π‘₯) ) =∫1▒𝑑𝑑/cos^2⁑𝑑 . 𝑑𝑑 =∫1β–’sec^2⁑𝑑 . 𝑑𝑑 =tan⁑𝑑+𝐢 Putting value of 𝑑=π‘₯𝑒^π‘₯ =tan⁑(π‘₯𝑒^π‘₯ )+𝐢 Hence B is correct answer

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.