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Prove that the curves y2 = 4x and x2 = 4y divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts. ?

Prove that the curves y2 = 4x and x2 = 4y divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.
?

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
Area of square ‘A’:
A = 4 \times 4 =16
Area b/w curves ‘a’:
a = \int_{0}^{4}(2\sqrt{x} - \frac{x^{2}}{4})dx
a = (\frac{4x^{3/2}}{3}-\frac{x^{3}}{12})_{0}^{4} = \frac{32}{3}-\frac{16}{3} = \frac{16}{3}
Area of rest two parts:
A -a = \frac{32}{3}
which is equally divided into 16/3 & 16/3.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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