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The parabolas y^(2)=4x and x^(2)=4y divi...

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 the areas of these parts numbered from top to bottom, respectively, then

A

`S_(1):S_(2)equiv1:1`

B

`S_(2):S_(3)equiv1:2`

C

`S_(1):S_(3)equiv1:1`

D

`S_(1):(S_(1)+S_(2))=1:2`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`y^(2)=4x and x^(2)=4y" meet at "O(0,0) and A(4,4).`

`"Now, "S_(3)=int_(0)^(4)(x^(2))/(4)dx=(1)/(4)[(x^(3))/(3)]_(0)^(4)=(1)/(12)[64-0]=(16)/(3).`
`S_(2)=int_(0)^(4)2sqrt(x)dx-S_(3)=2[(x^(3//2))/(3//2)]-(16)/(3)`
`=(4)/(3)[8-0]-(16)/(3)=(16)/(3).`
`"And "S_(1)=4xx4-(S_(2)+S_(3))=16-((16)/(3)+(16)/(3))=(16)/(3).`
`"Hence, "S_(1):S_(2):S_(3)=1:1:1`
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