JEE PYQ: Area Under Curves Question 10
Question 10 - 2021 (26 Feb Shift 2)
Let $A_1$ be the area of the region bounded by the curves $y = \sin x$, $y = \cos x$ and $y$-axis in the first quadrant. Also, let $A_2$ be the area of the region bounded by the curves $y = \sin x$, $y = \cos x$, $x$-axis and $x = \frac{\pi}{2}$ in the first quadrant. Then,
(1) $A_1 = A_2$ and $A_1 + A_2 = \sqrt{2}$
(2) $A_1 : A_2 = 1 : 2$ and $A_1 + A_2 = 1$
(3) $2A_1 = A_2$ and $A_1 + A_2 = 1 + \sqrt{2}$
(4) $A_1 : A_2 = 1 : \sqrt{2}$ and $A_1 + A_2 = 1$
Show Answer
Answer: (4) $A_1 : A_2 = 1 : \sqrt{2}$ and $A_1 + A_2 = 1$
Solution
$A_1 + A_2 = \int_0^{\pi/2} \cos x,dx = 1$. $A_1 = \sqrt{2} - 1$, $A_2 = 2 - \sqrt{2}$. $A_1/A_2 = 1/\sqrt{2}$.
BETA
