12th Class
Mathematics
Definite Integrals
Question Bank
Critical Thinking
question_answer
Let \[f(x)\] be a function satisfying \[{f}'(x)=f(x)\] with \[f(0)=1\] and \[g(x)\] be the function satisfying \[f(x)+g(x)={{x}^{2}}.\] The value of integral \[\int_{0}^{1}{f(x)\,g(x)\,dx}\] is equal to [AIEEE 2003; DCE 2005]
A)\[\frac{1}{4}(e-7)\]
B)\[\frac{1}{4}(e-2)\]
C)\[\frac{1}{2}(e-3)\]
D)None of these
Correct Answer:
D
Solution :
We have \[f'(x)=f(x)\Rightarrow \frac{f'(x)}{f(x)}=1\]