Q. 165.0( 2 Votes )
Prove that the curves y2 = 4x and x2 = 4y divide the area of the square bounded by x = 0, y = 0, x = 4 and y = 4 into three equal parts. [CBSE 2015, 2016]
Answer :
Given; y2 = 4x and x2 = 4y
By solving 
Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by 
.
Area of middle region
Area of lower region
Area of the upper region
= Area of Square − Area of middle region − Area of lower region
∴ The curves y2 = 4x and x2 = 4y divide the area of the square bounded by x = 0, y = 0, x = 4 and y = 4 into three equal parts
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