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Ex 7.2, 10 - Chapter 7 Class 12 Integrals
Last updated at May 29, 2023 by Teachoo
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Transcript
Ex 7.2, 10 Integrate the function: 1𝑥 − 𝑥 Step 1: Simplify the given function 1𝑥 − 𝑥 = 1 𝑥 𝑥 − 1 Step 2: 𝑥 − 1=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 12 . 𝑥 12 − 1−0= 𝑑𝑡𝑑𝑥 12 . 𝑥− 12= 𝑑𝑡𝑑𝑥 𝑑𝑥= 2 𝑑𝑡 𝑥− 12 𝑑𝑥=2 𝑥 𝑑𝑡 Step 3: Integrating the function 1𝑥 − 𝑥 . 𝑑𝑥 = 1 𝑥 𝑥 − 1 . 𝑑𝑥 putting 𝑡= 𝑥 − 1 & 𝑑𝑥=2 𝑥 𝑑𝑡 = 1 𝑥 𝑡 . 2 𝑥 . 𝑑𝑥 = 2𝑡 . 𝑑𝑡 = 2 1𝑡 . 𝑑𝑡 = 2 log 𝑡+𝐶 = 𝟐 𝒍𝒐𝒈 𝒙 −𝟏+𝑪
