Question

The parabolas $y^2=4x$ and $x^2=4y$ divide the square region bounded by the lines $x=4,y=4$ and the coordinate axes. If $S_1$, $S_2$, $S_3$ are respectively the areas of these parts numbered from top to bottom; $S_1:S_2:S_3$ is

• A. $1:2:3$
• B. $1:2:1$
• C. $1:1:1$
• D. $2:1:2$

Answer 1

Answer: (C)

$1:1:1$

Total area $=4\times 4=16$ sq. units
Area of $S_3={\int }_0^4\frac{x^2}{4}dx=\frac{16}{3}=S_1$
$\therefore$ $S_2=16-\frac{16}{3}\times 2=\frac{16}{3}$
$\therefore$ $S_1:S_2:S_3$ is $1:1:1$