AP EAMCET202017 Sep 2020Morning ShiftMathematicsIndefinite IntegrationActual
( 2 (x) 1+2 ^2(x) d x= )
Options
- A( | ^2 x+ ^2 x |+c )
- B( | ^2 x 2 + ^2 x |+c )
- C( | ^2 x+ ^2 x 2 |+c )
- D( | ^2 x 2 + ^2 x 2 |+c )
Correct answer
B. ( | ^2 x 2 + ^2 x |+c )
Step-by-step solution
( aligned & ( 2 x 1+2 ^2 x ) d x= 2 x x ^2 x+2 ^2 x d x & 2 x x 1+ ^2 x d x aligned ) Let (1+ ^2 x=t 2 x x d x=d t ) ( aligned d t t & = |t|+c₁= |1+ ^2 x |+c₁ & = |2 ^2 x+ ^2 x |+c₁ aligned ) ( aligned & 2 | ^2 x+ ^2 x 2 |+c₁ & 2+ | ^2 x+ ^2 x 2 |+c₁ & | ^2 x 2 + ^2 x |+c [ 2+c₁=c ] aligned )