Question 28 (Choice 1) - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Feb. 10, 2025 by Teachoo

Find : ∫√(x/(1-x^3 )) dx; x∈(0,1)

This question is similar to Misc 12 Chapter 7 Class 12

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Transcript

∫√(𝑥/(1 − 𝑥^3 )) 𝑑𝑥 = ∫1▒√𝑥/√(1 − 𝑥^3 ) 𝑑𝑥 Let 𝒕=𝒙^(𝟑/𝟐) Differentiating w.r.t. 𝑥 𝑑𝑡/𝑑𝑥=3/2 𝑥^(3/2 −1) 𝑑𝑡/𝑑𝑥=3/2 𝑥^(1/2 ) 𝑑𝑡/𝑑𝑥=3/2 √𝑥 𝟐/𝟑 𝐝𝐭=√𝒙 𝒅𝒙 Now, our equation becomes ∫1▒√𝑥/√(1 − 𝑥^3 ) 𝑑𝑥=∫1▒〖2/(3√(1 −〖 𝑥〗^3 )) 𝑑𝑡〗 = 𝟐/𝟑 ∫1▒𝒅𝒕/√(𝟏 − 𝒕^𝟐 )dt = 2/3 sin^(−1)⁡〖𝑡+𝑐〗 Putting back 𝑡=𝑥^(3/2) = 𝟐/𝟑 〖𝒔𝒊𝒏〗^(−𝟏)⁡〖〖(𝒙〗^(𝟑/𝟐))+𝒄〗

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

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