AP EAMCET202420 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
If 3 2 ^3 x 2 2 x d x= 3 2 ( x)^B+ 1 10 ( x)^A+c then A =
Options
- A1 2
- B1
- C5
- D5 2
Correct answer
D. 5 2
Step-by-step solution
3 2 ^3 x 2 2 x = 3 2 ^3 x 4 x 1+ ^2 x I= 3 ^4 x 4 x d x= 3 4 (1+ ^2 x ) x ^2 x d x x= t d t= ^2 x d xI= 3 4 ( 1 t +t^ 3 / 2 ) d t= 3 4 [2 t + 2 5 t^ 5 / 2 ]+C= 3 4 [2 x + 2 5 ( x)^ 5 / 2 ]+C= 3 2 ( x)^ 1 / 2 + 3 10 ( x)^ 5 / 2 +C A= 5 2