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MHT CET202123 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual

10^ x 2 10^ -x -10^x d x=

Options

  1. A2 10^ -x -10^x+c
  2. B1 10 ⁻¹ (10^x )+c
  3. C2 10^ -x +10^x+c
  4. D1 10 ⁻¹ (10^x )+c

Correct answer

B. 1 10 ⁻¹ (10^x )+c

Step-by-step solution

Let I= 10^ x 2 10^ -x -10^x d x aligned & = 10^ x 2 1 10^x -10^x d x= 10^ x 2 1- (10^x )^2 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) dx = dt I = 1 10 dt 1- t ^2 = 1 10 ⁻¹( t )+ c = 1 10 ⁻¹ (10^ x )+ c

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