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AP EAMCET2005MathematicsArea Under Curves

The area (in square units) bounded by the curves y^2=4 x and x^2=4 y in the plane is

Options

  1. A8 3
  2. B16 3
  3. C32 3
  4. D64 3

Correct answer

A. 8 3

Step-by-step solution

Given curves are The intersecting points of Eqs. (i) and (ii) are (0,0) and (4,4) Required area = Area of shaded portion O A B C aligned & = ₀^4 ( 4 x - x^2 4 ) d x & = [ 2 x^ 3 / 2 3 / 2 - x^3 12 ]₀^4 & = [ 4 3 8- 64 12 ]= [ 32 3 - 16 3 ] aligned = 16 3 sq. units.

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