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AP EAMCET202420 May 2024Morning ShiftMathematicsArea Under CurvesActual

Area of the region (in square units) enclosed by the curves y^2=8(x+2), y^2=4(1-x) and the Y -axis is

Options

  1. A8 3 (5-3 2 )
  2. B8 3 ( 2 -1)
  3. C8 3 (3- 2 )
  4. D4 3 ( 2 +1)

Correct answer

A. 8 3 (5-3 2 )

Step-by-step solution

y^2=8(x+2)y^2=4(1-x) The area of the required region is A=2 [ _ -2 ⁻¹ y₁ d x+ _ -1 ^0 y₂ d x ] where y₁= 8(x+2) =2 2 (x+2)^ 1 / 2 and y₂= 4(1-x) =2(1-x)^ 1 / 2 A=2 [ _ -2 ⁻¹ 2 2 (x+2)^ 1 / 2 d x+2 _ -1 ^0(1-x)^ 1 / 2 d x ]=2 [2 2 [ (x+2)^ 3 / 2 3 / 2 ]_ -2 ⁻¹+2 -2 3 (1-x)^ 3 / 2 _ -1 ^0 ]=2 [2 2 2 3 + 2 2 3 (2 2 -1) ]= 8 3 [ 2 +2 2 -1]= 8 3 [3 2 -1]

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