AP EAMCET20228 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual
( x+ 12 x-36 + x- 12 x-36 ) d x=
Options
- A2 3 x+C, x
- B4(x-3)^ 3 / 2 3 +C, x
- Carray ccc 4 3 (x-3)^ 3 / 2 +C, & if & x>6 2 3 x+C & if & 3 x 6 array .
- Darray ccc 4 3 (x-3)^ 3 / 2 +C, & if & 3 x 6 2 3 x+C & if & x>6 array .
Correct answer
C. array ccc 4 3 (x-3)^ 3 / 2 +C, & if & x>6 2 3 x+C & if & 3 x 6 array .
Step-by-step solution
I= ( x+ 12 x-36 + x- 12 x-36 d x Put t^2=12 x-36 x= t^2+36 12 and 2 t d t=12 d x t d t=6 d xI= ( t^2+36 12 +t + t^2+36 12 -t ) ( t 6 ) d tI= 1 6 (t+6)+(t-6) 12 t d t [ . when .t^2>36 ] aligned & = 1 6 12 (2 t) t d t= 1 3 12 t^2 d t & = 1 3 12 ( t^3 3 )+C= 1 9 12 (12 x-36)^ 3 2 +C & = (1.2)^ 3 / 2 9(12)^ 1 / 2 (x-3)^ 3 / 2 +C= 12 9 (x-3)^ 3 / 2 +C & = 4 3 (x-3)^ 3 / 2 +C, if x>6 aligned Now, I= 1 6 12 t+6-(t-6) t d t[3 x 6] aligned & = 1 6 12 12 t d t= 12 6 t d t & = 12 6 ( t^2 2 )+C^ = 1 12 (12 x-36)+C^ & = 12 x+ (