AP EAMCET2006MathematicsIndefinite Integration
Observe the following statements : A : ( x^2-1 x^2 ) e^ x^2+1 x d x=e^ x^2+1 x +c R : f^ (x) e^ f(x) d x=f(x)+c Then which of the following is true ?
Options
- ABoth A and R are true and R is not the correct reason for A
- BBoth A and R are true and R is the correct reason for A
- CA is true, R is false
- DA is false, R is true
Correct answer
C. A is true, R is false
Step-by-step solution
(A) Let I= ( x^2-1 x^2 ) e^ ( x^2+1 x ) d x= (1- 1 x^2 ) e^ (x+ 1 x ) d x Let x+ 1 x =t (1- 1 x^2 ) d x=d t I= e^t d t=e^t+c=e^ x+ 1 x +c=e^ x^2+1 x +c (R) Let I= f^ (x) e^ f(x) d x Let f(x)=tf^ (x) d x=d t I= e^t d t=e^t+c=e^ f(x) +c Thus A is true but R is false.