Ex 7.3, 9 - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Ex 7.3
Ex 7.3, 2
Ex 7.3, 3 Important
Ex 7.3, 4 Important
Ex 7.3, 5
Ex 7.3, 6 Important
Ex 7.3, 7
Ex 7.3, 8
Ex 7.3, 9 Important You are here
Ex 7.3, 10 Important
Ex 7.3, 11
Ex 7.3, 12
Ex 7.3, 13 Important
Ex 7.3, 14
Ex 7.3, 15
Ex 7.3, 16 Important
Ex 7.3, 17
Ex 7.3, 18 Important
Ex 7.3, 19 Important
Ex 7.3, 20 Important
Ex 7.3, 21
Ex 7.3, 22 Important
Ex 7.3, 23 (MCQ)
Ex 7.3, 24 (MCQ) Important
Last updated at April 16, 2024 by Teachoo
Ex 7.3, 9 Integrate (𝑐𝑜𝑠 𝑥)/(1 + 𝑐𝑜𝑠 𝑥) ∫1▒〖(𝑐𝑜𝑠 𝑥)/(1 + 𝑐𝑜𝑠 𝑥) " " 𝑑𝑥〗 = ∫1▒((cos𝑥 + 1 − 1)/(1 + cos𝑥 )) 𝑑𝑥 =∫1▒((1 + cos𝑥 − 1)/(1 + cos𝑥 )) 𝑑𝑥 =∫1▒((1 + cos𝑥)/(1 + cos𝑥 ) − 1/(1 + cos𝑥 )) 𝑑𝑥 =∫1▒〖1−1/(1 + cos𝑥 )〗 𝑑𝑥 =∫1▒1 𝑑𝑥−∫1▒𝟏/(𝟏 + 𝒄𝒐𝒔𝒙 ) 𝑑𝑥 =∫1▒1 𝑑𝑥−∫1▒1/(𝟐 〖𝒄𝒐𝒔〗^𝟐〖𝒙/𝟐〗 ) 𝑑𝑥 =∫1▒1 𝑑𝑥−∫1▒1/2 sec^2〖𝑥/2〗 𝑑𝑥 =∫1▒1 𝑑𝑥−1/2 ∫1▒sec^2〖𝑥/2〗 𝑑𝑥 =𝑥− 1/2 〖tan 〗〖𝑥/2〗/(1/2) +𝐶 =𝑥− 2/2 〖tan 〗〖𝑥/2〗 +𝐶 =𝒙− 〖𝐭𝐚𝐧 〗〖𝒙/𝟐〗 +𝑪 ∫1▒sec^2(𝑎𝑥+𝑏) 𝑑𝑥=𝑡𝑎𝑛(𝑎𝑥 + 𝑏)/𝑎 +𝐶 We know that cos 2𝜃=2 cos^2〖𝜃−1〗 cos2𝜃+1=2 cos^2𝜃 Replacing 𝜃 by 𝑥/2 cos2(𝑥/2)+1=2 cos^2〖𝑥/2〗 cos𝑥+1=2 cos^2〖𝑥/2〗