KCET2017MathematicsMathematical Reasoning
( ₀^ 2 1 a² ² x+b² ² x d x ) is equal to
Options
- A( a 4 b )
- B( a 2 b )
- C( b 4 a )
- D( 2 a b )
Correct answer
D. ( 2 a b )
Step-by-step solution
[ array l Given that, ₀^ / 2 1 a² ² x+b² ² x d x = ₀^ / 2 1 ² x ² x +b² ² x ² x d x = ₀^ / 2 ² x a² ² x+b² d x array ] Let ( x =t ) then, ( d t= ² x d x ) and limits change from ( 0 0, 2 ) [ array l 1 a² ₀^ d t 1+ ( b a )² t² = 1 a² 1 (b / a) ( ⁻¹ ( t b / a ) ) = 1 a b ( 2 -0 )= 2 a b array ]