# Misc 42 - Chapter 7 Class 12 Integrals

Last updated at May 29, 2018 by Teachoo

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.

Miscellaneous

Misc 1

Misc 2

Misc 3

Misc 4

Misc 5

Misc 6

Misc 7

Misc 8 Important

Misc 9

Misc 10

Misc 11

Misc 12

Misc 13

Misc 14

Misc 15

Misc 16

Misc 17

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21

Misc 22

Misc 23

Misc 24 Important

Misc 25

Misc 26

Misc 27

Misc 28

Misc 29

Misc 30 Important

Misc 31

Misc 32 Important

Misc 33

Misc 34

Misc 35

Misc 36

Misc 37

Misc 38

Misc 39

Misc 40

Misc 41 Important

Misc 42 You are here

Misc 43

Misc 44 Important

Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

About the Author

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.