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Ex 7.2, 7 - Integrate x root (x+2) - Teachoo Maths - Ex 7.2

Ex 7.2, 7 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.2, 7 - Chapter 7 Class 12 Integrals - Part 3

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Ex 7.2, 7 Integrate the function: π‘₯√(π‘₯+2) π‘₯√(π‘₯+2) Step 1: Let (π‘₯+2)=𝑑 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ 1+0 = 𝑑𝑑/𝑑π‘₯ 1= 𝑑𝑑/𝑑π‘₯ 𝑑π‘₯=𝑑𝑑 Step 2: Integrating the function ∫1β–’γ€–" " π‘₯√(π‘₯+2)γ€— .𝑑π‘₯ Putting the value of π‘₯+2 & 𝑑π‘₯ . = ∫1β–’γ€–π‘₯βˆšπ‘‘γ€— .𝑑π‘₯ = ∫1β–’γ€–π‘₯βˆšπ‘‘γ€— .𝑑𝑑 = ∫1β–’γ€–(π‘‘βˆ’2) βˆšπ‘‘γ€— .𝑑𝑑 = ∫1β–’γ€–(π‘‘βˆ’2) 𝑑^(1/2) γ€— .𝑑𝑑 = ∫1β–’(𝑑.𝑑^(1/2)βˆ’2.𝑑^(1/2) ) .𝑑𝑑 = ∫1β–’(𝑑^(3/2)βˆ’2.𝑑^(1/2) ) .𝑑𝑑 = ∫1▒𝑑^(3/2) .𝑑𝑑 βˆ’ 2∫1▒𝑑^(1/2) .𝑑𝑑 (Using π‘₯+2=𝑑, π‘₯=π‘‘βˆ’2) = 𝑑^(3/2 + 1)/(3/2 + 1) βˆ’ 2 . 𝑑^(1/2 + 1)/(1/2 + 1) + 𝐢 = 𝑑^(5/2)/(5/2) βˆ’ 2 . 𝑑^(3/2)/(3/2) + 𝐢 = 2/5 𝑑^(5/2) βˆ’ 2 Γ— 2/3 𝑑^(3/2) + 𝐢 = 2/5 𝑑^(5/2) βˆ’ 4/3 𝑑^(3/2) + 𝐢 Putting back 𝑑=π‘₯+2 = 𝟐/πŸ“ (𝒙+𝟐)^(πŸ“/𝟐) βˆ’ πŸ’/πŸ‘ (𝒙+𝟐)^(πŸ‘/𝟐) + π‘ͺ (Using ∫1β–’π‘₯^𝑛 . 𝑑π‘₯=π‘₯^(𝑛+1)/(𝑛 +1) )

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.