AP EAMCET202021 Sep 2020Morning ShiftMathematicsIndefinite IntegrationActual
Let the equation of the curve passing through the point ((0,1) ) be given by (y= x^3 e^ x^4 d x ). If the equation of the curve is written in the form (x=f(y) ), then (f(y)= )
Options
- A( |4 y-3| )
- B(( |4 y-3|)^ 1 / 4 )
- C( ( | 3-4 y 4 | )^ 1 / 4 )
- D( | 4 y-3 4 | )
Correct answer
B. (( |4 y-3|)^ 1 / 4 )
Step-by-step solution
It is given that, (y= x^3 e^ x^4 d x ) Let (x^4=t 4 x^3 d x=d t ) ( ) So, (y= 1 4 e^t d t= e^t 4 +C= e^ x^4 4 +C ) ( ) The curve (y= e^ x^4 4 +C ) passes through point ((0,1) ), so (C= 3 4 y= e^ x^4 4 + 3 4 e^ x^4 =4 y-3 ) ( x^4= _e|4 y-3| x= ( _e|4 y-3| )^ 1 / 4 ) Hence, option (c) is correct.