MHT CET202016 Oct 2020Morning ShiftMathematicsIndefinite IntegrationActual
f x- 1 x ( x²+1 x² ) d x= 2 3 (x- 1 x )^ k +c , then value of k is
Options
- A2 3
- B3 2
- C5 2
- D2 5
Correct answer
B. 3 2
Step-by-step solution
(C) array l Let I = x - 1 x ( x ²+1 x ² ) d x = 2 3 ( x - 1 x )^ k + c Put x - 1 x = t 1 2 x - 1 x (1+ 1 x ² ) dx = dt ( x ²+1 x ² ) d x =2 t dt I = t (2 t ) dt =2 t ² dt = 2 t ³ 3 = 2 3 [ x - 1 x ]³ = 2 3 [ ( x - 1 x )^ 1 2 ]³= 2 3 [ x - 1 x ]^ 3 2 k = 3 2 array