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Prove that the curves y^2=4x\ a n d\ x^2...

Prove that the curves `y^2=4x\ a n d\ x^2=4y` divide the area of the square bounded by `x=0,\ y=0,\ x=4\ n d\ y=4` into three equal parts.

Text Solution

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To prove
`A_1 =A_2= A_3 =A/3` [ A= area of square]
`A= 4xx4 = 16` sq. units
`A_1 = int_0^4 x^2/(4) dx = 16/3` sq.units
`A_2 = int_0^4 y^2/(4) dy = 16/3`
`A_3 =A-(A_1 -A_2)`
`= 16 - 2xx(16)/3`
`= (16)/3` sq.units
Hence proved
`A_1 =A_2= A_3 =A/3`
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