NDA2024MathematicsIndefinite IntegrationActual
Let d x x+1 - x-1 = (x+1)^ 3 2 + (x-1)^ 3 2 +c What is the value of ?
Options
- A1 3
- B2 3
- C1
- D4 3
Correct answer
A. 1 3
Step-by-step solution
Given, d x x+1 - x-1 = (x+1)^ 3 2 + (x-1)^ 3 2 +c ....(i) Let, I = d x x+1 - x-1 aligned & = ( x+1 + x-1 ) d x ( x+1 - x-1 )( x+1 + x-1 ) & I = 1 2 (x+1) d x+ 1 2 x-1 d x & I = 1 2 (x+1)^ 3 2 ( 3 2 ) + 1 2 (x-1)^ 3 2 ( 3 2 ) +c & I = 1 3 (x+1)^ 3 2 + 1 3 (x-1)^ 3 2 +c & d x x+1 - x-1 = 1 3 (x+1)^ 3 2 + 1 3 (x-1)^ 3 2 +c (ii) aligned From (i) and (ii) we get = 1 3