Q. The set of values of $\alpha(\alpha > 0)$ for which the inequality $\int_{- \alpha}^{\alpha}{e^{x}dx > \frac{3}{2}}$ holds true, is
A) $(0,\infty)$
B) $(2,\infty)$
C) $(\log 2,\infty)$
D) None of these
Explanation
(c)
Since, $2e^{2\alpha} - 3e^{\alpha} - 2 > 0$
$\Rightarrow \ e^{\alpha} < - \frac{1}{2}\$ or $e^{\alpha} > 2$
But $e^{\alpha} > 0,\ \forall\alpha\ \in R \Rightarrow e^{\alpha} > 2$
$\therefore\ \alpha \in (\log{2,\ \infty)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.