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COMEDK2018MathematicsIndefinite Integration

The value of 10^ x / 2 10^ -x -10^ x d x is

Options

  1. A1 _ 10 ⁻¹ (10^ x )+c
  2. B2 10^ -x +10^ x +c
  3. C1 _ e 10 ⁻¹ (10^ x )+c
  4. D-1 _ e 10 ⁻¹ (10^ x )+c

Correct answer

A. 1 _ 10 ⁻¹ (10^ x )+c

Step-by-step solution

Let aligned I &= 10^ x / 2 10^ -x -10^ x d x &= 10^ x / 2 1 10^ x -10^ x d x= 10^ x / 2 10^ x / 2 1- (10^ x )² d x &= 10^ x 1- (10^ x )² d x aligned Put 10^ x =t 10^ x 10 d x=d t aligned So , I &= 1 10 d t 1-t² &= 1 10 ⁻¹(t)+c= 1 10 ⁻¹ (10^ x )+c aligned

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