Integral Calculus Question 128
Question: Let $ f(x)=\int{e^{x}(x-1)(x-2)}dx $ . Then f decreases in the interval
Options:
A) $ (-\infty ,-2) $
B) $ (-2,-1) $
C) $ (1,2) $
D) $ (2,+\infty ) $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ f(x)=\int{e^{x}(x-1)(x-2)dx} $ For decreasing function, $ f’(x)<0 $
$ \Rightarrow e^{x}(x-1)(x-2)<0 $
$ \Rightarrow (x-1)(x-2)<0 $
$ \Rightarrow 1<x<2 $
$ \therefore e^{x}>0\forall x\in R $
BETA
