Prove that the curves y2 = 4x and x2 = 4y divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.
A1, A2, A3 are the areas denoted in the figure. We need to prove A1 = A2 = A3.
`A_1 = ∫_0^4y1dx`
`= ∫_0^4x^2/4dx `
`=16/3 sq. units`
`A_3=area bounded by y^2=4x, y=0 and y=4`
`therefore A_1=A_2 =A_3 =16/3 sq. units`
Thus, y2 = 4x and x2 = 4y divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.
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