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AP EAMCET2014MathematicsDefinite Integration

₀^ 6 ^4 3 ^2 6 d equals to

Options

  1. A96
  2. B5 192
  3. C5 256
  4. D5 192

Correct answer

D. 5 192

Step-by-step solution

Let I= ₀^ / 6 ^4 3 ^2 6 d Put 3 =t d = d t 3 aligned I & = 1 3 ₀^ / 2 ^4 t ^2 2 t d t & = 1 3 ₀^ / 2 ^4 t (2 t t)^2 d t & = 4 3 ₀^ ^6 t ^2 t d t & = 4 3 [ 5 3 1 8 6 4 2 2 ] aligned [use gamma rule of integration] = 5 192

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