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COMEDK2012MathematicsDefinite Integration

If _ 2 ^ x d y e^ y -1 = 6 , then x is equal to

Options

  1. A_ e 4
  2. B_ e 2
  3. C4
  4. D2

Correct answer

A. _ e 4

Step-by-step solution

We have, _ 2 ^ x 1 e^ y -1 d y= 6 Let e^ y -1 =t e^ y -1=t² e^ y =1+t² e^ y d y=2 t d t (1+t² ) d y=2 t d t d y= 2 t (1+t² ) d t Now, ₁^ e^ x-1 2 t (1+t² ) t d t= 6 array lc & ₁^ e^ x -1 d t 1+t² = 12 & [ ⁻¹ t ]₁^ e^ x -1 = 12 & ⁻¹ e^ x -1 - 4 = 12 & ⁻¹ e^ x -1 = 3 & ( ⁻¹ e^ x -1 )= ( 3 ) & e^ x -1=3 e^ x =4 & x= 4 array

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