Integration Full Chapter Explained - Integration Class 12 - Everything you need

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 42 Choose the correct answer cos2𝑥sin𝑥 + cos𝑥2 𝑑𝑥 is equal to (A) −1sin𝑥 + cos𝑥+𝐶 (B) logsin𝑥+cos𝑥+𝐶 (C) logsin𝑥−cos𝑥+𝐶 (D) 1sin𝑥 + cos𝑥2 cos2𝑥cos𝑥 + sin𝑥2 =cos2𝑥 − sin2𝑥cos𝑥 + sin𝑥2 𝑑𝑥 =cos𝑥 − sin𝑥cos𝑥 + sin𝑥cos𝑥 + sin𝑥2 𝑑𝑥 =cos𝑥 − sin𝑥cos𝑥 + sin𝑥 𝑑𝑥 Let cos𝑥+sin𝑥=𝑡 Diff w.r.t. x −sin𝑥+cos𝑥=𝑑𝑡𝑑𝑥 𝑑𝑥=1cos𝑥 − sin𝑥 𝑑𝑡 Hence, our equation becomes =cos𝑥 − sin𝑥𝑑𝑡 ×𝑑𝑡cos𝑥 − sin𝑥 =1𝑡 𝑑𝑡 =log𝑡+𝐶 Putting value of 𝑡=𝑐𝑜𝑠𝑥+𝑠𝑖𝑛𝑥 =logcos𝑥+sin𝑥+𝐶 Hence correct answer is B.

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Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.