Integral Calculus Question 95
Question: Let $ f(0)=0 $ and $ \int\limits_0^{2}{f’(2t){e^{f(2t)}}dt=5} $ . Then the value of f(4) is
Options:
A) log 2
B) log 7
C) log 11
D) log 13
Show Answer
Answer:
Correct Answer: C
Solution:
[c] We have $ \int\limits_0^{2}{f’(2t){e^{f(2t)}}dt=5} $ Put $ {e^{f(2t)}}=y $
$ \therefore 2f’(2t){e^{f(2t)}}dt=dy $
$ \therefore \frac{1}{2}\int\limits_{{e^{f(0)}}}^{{e^{f(4)}}}{dy=5} $ Or $ \int\limits_{{e^{f(0)}}}^{{e^{f(4)}}}{dy=10} $ Or $ {e^{f(4)}}-{e^{f(0)}}=10 $ Or $ {e^{f(4)}}=10+1=11 $ Or $ f(4)=log11 $
BETA
