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 August 2, 2026 by Teachoo

Find : ∫√(x/(1-x^3 )) dx; x∈(0,1)

This question is similar to Misc 12 Chapter 7 Class 12

[Class 12] Find ∫ √(x/1-x^3) dx - Teachoo Sample Paper (with Video) - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 28 (Choice 1) - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

Next: Question 28 (Choice 2) Important → Remove Ads

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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