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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

  1. A1 2
  2. B1
  3. C5
  4. 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

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