Definite Integration Question 251
Question: If $ f(x)=\int _{x^{2}}^{x^{2}+1}{{e^{-t^{2}}}}dt, $ then $ f(x) $ increases in
[IIT Screening 2003]
Options:
A) $ (2,2) $
B) No value of $ x $
C) $ (0,\infty ) $
D) $ (-\infty ,0) $
Show Answer
Answer:
Correct Answer: D
Solution:
$ f’(x)={e^{-{(x^{2}+1)^{2}}}}\cdot2x-{e^{-{(x^{2})^{2}}}}\cdot2x=2x{e^{-(x^{4}+2x^{2}+1)}}( 1-{e^{2x^{2}+1}} ) $
therefore $ f’(x)>0,\forall x\in (-\infty ,0). $
BETA
