Ex 7.2, 1 - Chapter 7 Class 12 Integrals (Term 2)
Last updated at Dec. 11, 2021 by Teachoo
Ex 7.2
Ex 7.2, 1
You are here
Ex 7.2, 2
Ex 7.2, 3 Important
Ex 7.2, 4
Ex 7.2, 5 Important
Ex 7.2, 6
Ex 7.2, 7 Important
Ex 7.2, 8
Ex 7.2, 9
Ex 7.2, 10 Important
Ex 7.2, 11 Important
Ex 7.2, 12
Ex 7.2, 13
Ex 7.2, 14 Important
Ex 7.2, 15
Ex 7.2, 16
Ex 7.2, 17
Ex 7.2, 18
Ex 7.2, 19 Important
Ex 7.2, 20 Important
Ex 7.2, 21
Ex 7.2, 22 Important
Ex 7.2, 23
Ex 7.2, 24
Ex 7.2, 25
Ex 7.2, 26 Important
Ex 7.2, 27
Ex 7.2, 28
Ex 7.2, 29 Important
Ex 7.2, 30
Ex 7.2, 31
Ex 7.2, 32 Important
Ex 7.2, 33 Important
Ex 7.2, 34 Important
Ex 7.2, 35
Ex 7.2, 36 Important
Ex 7.2, 37
Ex 7.2, 38 (MCQ) Important
Ex 7.2, 39 (MCQ) Important
Transcript
Ex 7.2, 1 Integrate the function: 2𝑥/(1 + 𝑥2) We need to find ∫1▒𝟐𝒙/(𝟏 + 𝒙𝟐) 𝒅𝒙 Let 𝟏 + 𝒙𝟐 = 𝒕 Differentiating 𝑤.𝑟.𝑡.𝑥 2𝑥=𝑑𝑡/𝑑𝑥 𝒅𝒙=𝒅𝒕/𝟐𝒙 Thus, our equation becomes ∫1▒𝟐𝒙/(𝟏 + 𝒙𝟐) 𝒅𝒙 =∫1▒2𝑥/𝑡 . 𝑑𝑡/2𝑥 =∫1▒𝑑𝑡/𝑡 = log |𝒕|+𝑪 Putting t = 1 + x2 = log |1+𝑥^2 |+𝐶 = log (𝟏+𝒙^𝟐 )+𝑪 (∫1▒〖1/𝑥 𝑑𝑥〗=log|𝑥|+𝐶) (Since 1+𝑥^2 is always positive)
