AP EAMCET202315 May 2023Evening ShiftMathematicsIndefinite IntegrationActual
If 1 x [( x)^2+4 x-1 ] d x=A [ x+B x+C ]+K where K is the constant of integration, then
Options
- AA = 1 2 5 , ~B =(2- 5 ), C =(2+ 5 )
- BA=- 1 2 5 , B=(2- 5 ), C=(2+ 5 )
- CA= 1 2 5 , B=(2+ 5 ), C=(2- 5 )
- DA=- 1 2 5 , B=(2+ 5 ), C=(2- 5 )
Correct answer
A. A = 1 2 5 , ~B =(2- 5 ), C =(2+ 5 )
Step-by-step solution
Let I= 1 x [( x)^2+4 x-1 ] d x aligned & =A [ x+B x+C ]+K & let x=t 1 x d x=d t & I= 1 t^2+4 t-1 d t= d t (t+2)^2-( 5 )^2 & = 1 2 5 [ x+2- 5 x+2+ 5 ] & A= 1 2 5 , B=2- 5 , C=2+ 5 aligned