AP EAMCET2002MathematicsIndefinite Integration
d x 1- x- x is equal to
Options
- A|1+ x 2 |+c
- B|1- x 2 |+c
- C|1- x 2 |+c
- D|1+ x 2 |+c
Correct answer
C. |1- x 2 |+c
Step-by-step solution
We have, aligned I & = d x 1- x- x & = d x 1- ( 1- ^2 x 2 1+ ^2 x 2 )- 2 x 2 1+ ^2 x 2 & = ^2 x 2 d x 1+ ^2 x 2 -1+ ^2 x 2 -2 x 2 aligned = 1 2 ^2 x 2 d x x 2 ( x 2 -1 ) Let x 2 =z aligned & 1 2 ^2 x 2 d x=d z & ^2 x 2 d x=2 d z & I= 1 2 2 d z z(z-1) = ( 1 z-1 - 1 z ) d z & = (z-1)- z+C & = ( z-1 z )+C= [ x 2 -1 x 2 ]+C & = [1- x 2 ]+C aligned