COMEDK2018MathematicsIndefinite Integration
The value of 10^ x / 2 10^ -x -10^ x d x is
Options
- A1 _ 10 ⁻¹ (10^ x )+c
- B2 10^ -x +10^ x +c
- C1 _ e 10 ⁻¹ (10^ x )+c
- 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