AP EAMCET202023 Sep 2020Morning ShiftPhysicsMotion in One DimensionActual
∫ 3 x 1 - 9 x d x =
Options
- Asin - 1 3 x · ( log 3 ) - 1 + c
- B- sin - 1 3 x · log 3 + c
- C1 3 sin - 1 3 x + c
- D1 9 sin - 1 3 x + c
Correct answer
A. sin - 1 3 x · ( log 3 ) - 1 + c
Step-by-step solution
Let I = ∫ 3 x 1 - 9 x d x = ∫ 3 x 1 - ( 3 x ) 2 d x Put 3 x = t , we get 3 x   log 3   d x = d t 3 x d x = 1 log 3 d t 3 x d x = ( log   3 ) - 1   d t I = ∫ ( log 3 ) - 1 1 - t 2 d t = ∫ 1 a 2 - x 2 d x =   sin - 1 ( x a ) + c ) I = ( log 3 ) - 1   S i n - 1 ( t ) + c Again put t = 3 x , we get I = ( log 3 ) - 1   S i n - 1 ( 3 x ) + c .