JEE PYQ: Application Of Derivatives Question 73
Question 73 - 2019 (10 Jan Shift 1)
Let $I = \int_a^b (x^4 - 2x^2),dx$. If $I$ is minimum then the ordered pair $(a, b)$ is:
(1) $(0, \sqrt{2})$
(2) $(-\sqrt{2}, 0)$
(3) $(\sqrt{2}, -\sqrt{2})$
(4) $(-\sqrt{2}, \sqrt{2})$
Show Answer
Answer: (4)
Solution
$\frac{dI}{da} = -(a^4 - 2a^2) = 0 \Rightarrow a = 0, \pm\sqrt{2}$. $\frac{dI}{db} = b^4 - 2b^2 = 0 \Rightarrow b = 0, \pm\sqrt{2}$. For minimum $I$: integrand is negative on $(-\sqrt{2}, \sqrt{2})$, so $(a,b) = (-\sqrt{2}, \sqrt{2})$.
BETA
