Applications Of Derivatives Question 47
Question: A minimum value of $ \int_0^{x}{t{e^{-t^{2}}}} $ dt is
[EAMCET 2003]
Options:
A) 1
B) 2
C) 3
D) 0
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=\int_0^{x}{t{e^{-t^{2}}}}dt\Rightarrow f’(x)=x{e^{-x^{2}}}=0\Rightarrow x=0 $
$ {f}’’(x)={e^{-x^{2}}}(1-2x^{2});\ \ \ {f}’’,(0)=1>0 $
$ \therefore $ Minimum value $ f(0)=0 $ .
BETA
