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The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to bottom; then S1 : S2 : S3 is ?

The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to bottom; then S1 : S2 : S3 is ?

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Area of square ‘A’:
A = 4 \times 4 =16
Area b/w curves ‘S2’:
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 S1& S3.
S_{1} = S_{2} = S_{3} = \frac{16}{3}
S_{1}:S_{2}:S_{3} = 1:1:1
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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