1. Tardigrade
  2. Question
  3. Mathematics
  4. Let f (x) = ∫ ex (x -1)(x - 2)dx . Then f decreases in the interval

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $f (x) = \int e^x (x -1)(x - 2)dx$ . Then f decreases in the interval

JEE AdvancedJEE Advanced 2000Application of Derivatives

Solution:

$f\left(x\right) =\int e^{x}\left(x-1\right)\left(x-2\right)dx $
For decreasing function $,f'\left(x\right)<0$
$ \Rightarrow e^{x}\left(x-1\right)\left(x-2\right) < 0 \Rightarrow \left(x -1\right)\left(x-2\right)<0 $
$\Rightarrow 1 < x < 2, \because e^{x} > 0 \forall x \in R$