CBSE Class 12 Sample Paper for 2024 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## Find : ∫√(x/(1-x^3 )) dx; x∈(0,1)

This question is similar to Misc 12 Chapter 7 Class 12

### Transcript

โซโ(๐ฅ/(1 โ ๐ฅ^3 )) ๐๐ฅ = โซ1โโ๐ฅ/โ(1 โ ๐ฅ^3 ) ๐๐ฅ Let ๐=๐^(๐/๐) Differentiating w.r.t. ๐ฅ ๐๐ก/๐๐ฅ=3/2 ๐ฅ^(3/2 โ1) ๐๐ก/๐๐ฅ=3/2 ๐ฅ^(1/2 ) ๐๐ก/๐๐ฅ=3/2 โ๐ฅ ๐/๐ ๐๐ญ=โ๐ ๐๐ Now, our equation becomes โซ1โโ๐ฅ/โ(1 โ ๐ฅ^3 ) ๐๐ฅ=โซ1โใ2/(3โ(1 โใ ๐ฅใ^3 )) ๐๐กใ = ๐/๐ โซ1โ๐๐/โ(๐ โ ๐^๐ )dt = 2/3 sin^(โ1)โกใ๐ก+๐ใ Putting back ๐ก=๐ฅ^(3/2) = ๐/๐ ใ๐๐๐ใ^(โ๐)โกใใ(๐ใ^(๐/๐))+๐ใ

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.