Check sibling questions

Ex 7.3, 9 - Integrate cos x / 1 + cos x - Class 12 CBSE - Ex 7.3

Ex 7.3, 9 - Chapter 7 Class 12 Integrals - Part 2

Get live Maths 1-on-1 Classs - Class 6 to 12


Transcript

Ex 7.3, 9 Integrate (π‘π‘œπ‘  π‘₯)/(1 + π‘π‘œπ‘  π‘₯) ∫1β–’γ€–(π‘π‘œπ‘  π‘₯)/(1 + π‘π‘œπ‘  π‘₯) " " 𝑑π‘₯γ€— = ∫1β–’((cos⁑π‘₯ + 1 βˆ’ 1)/(1 + cos⁑π‘₯ )) 𝑑π‘₯ =∫1β–’((1 + cos⁑π‘₯ βˆ’ 1)/(1 + cos⁑π‘₯ )) 𝑑π‘₯ =∫1β–’((1 + cos⁑π‘₯)/(1 + cos⁑π‘₯ ) βˆ’ 1/(1 + cos⁑π‘₯ )) 𝑑π‘₯ =∫1β–’γ€–1βˆ’1/(1 + cos⁑π‘₯ )γ€— 𝑑π‘₯ =∫1β–’1 𝑑π‘₯βˆ’βˆ«1β–’πŸ/(𝟏 + 𝒄𝒐𝒔⁑𝒙 ) 𝑑π‘₯ =∫1β–’1 𝑑π‘₯βˆ’βˆ«1β–’1/(𝟐 〖𝒄𝒐𝒔〗^πŸβ‘γ€–π’™/πŸγ€— ) 𝑑π‘₯ =∫1β–’1 𝑑π‘₯βˆ’βˆ«1β–’1/2 sec^2⁑〖π‘₯/2γ€— 𝑑π‘₯ =∫1β–’1 𝑑π‘₯βˆ’1/2 ∫1β–’sec^2⁑〖π‘₯/2γ€— 𝑑π‘₯ =π‘₯βˆ’ 1/2 γ€–tan 〗⁑〖π‘₯/2γ€—/(1/2) +𝐢 =π‘₯βˆ’ 2/2 γ€–tan 〗⁑〖π‘₯/2γ€— +𝐢 =π’™βˆ’ γ€–π­πšπ§ 〗⁑〖𝒙/πŸγ€— +π‘ͺ ∫1β–’sec^2⁑(π‘Žπ‘₯+𝑏) 𝑑π‘₯=π‘‘π‘Žπ‘›β‘(π‘Žπ‘₯ + 𝑏)/π‘Ž +𝐢 We know that cos 2πœƒ=2 cos^2β‘γ€–πœƒβˆ’1γ€— cos⁑2πœƒ+1=2 cos^2β‘πœƒ Replacing πœƒ by π‘₯/2 cos⁑2(π‘₯/2)+1=2 cos^2⁑〖π‘₯/2γ€— cos⁑π‘₯+1=2 cos^2⁑〖π‘₯/2γ€—

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.