MHT CET202123 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual
10^ x 2 10^ -x -10^x d x=
Options
- A2 10^ -x -10^x+c
- B1 10 ⁻¹ (10^x )+c
- C2 10^ -x +10^x+c
- 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