CUET Preparation Today
Let $f(x)=\int e^x(x-1)(x-2) d x$, then f(x) decreases in the interval |
$(-\infty,-2)$ $(-2,-1)$ $(1,2)$ $(2, \infty)$ |
$(1,2)$ |
We have, $f(x)=\int e^x(x-1)(x-2) d x \Rightarrow f'(x)=e^x(x-1)(x-2)$ For f(x) to be decreasing, we must have $f'(x)<0$ $\Rightarrow e^x(x-1)(x-2)<0 \Rightarrow(x-1)(x-2)<0 \Rightarrow x \in(1,2)$ |
