Definite Integration Question 319
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, then $ S_1:S_2:S_3 $ is
[AIEEE 2005]
Options:
A) $ 2:1:2 $
B) $ 1:1:1 $
C) $ 1:2:1 $
D) $ 1:2:3 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ y^{2}=4x $ and $ x^{2}=4y $ are symmetric about line $ y=x $
therefore Area bounded between $ y^{2}=4x $ and $ y=x $ is $ \int_0^{4}{(2\sqrt{x}-x)dx=\frac{8}{3}} $
therefore $ A _{s _{2}}=\frac{16}{3} $ and $ {A _{s_1}}={A _{S_3}}=\frac{16}{3} $
therefore $ {A _{S_1}}:{A _{S_2}}:{A _{S_2}}::1:1:1 $ .
BETA
