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MHT CET202124 Sep 2021Morning ShiftMathematicsArea Under CurvesActual

The area of the region include between the parabolas y^2=8 x and x ^2=8 y , is

Options

  1. A128 3 sq. units
  2. B64 3 sq. units
  3. C32 8 3 sq. units
  4. D16 8 3 sq. units

Correct answer

B. 64 3 sq. units

Step-by-step solution

Refer figure Required area is shaded. Point of intersection of given curves are y ^2=8 x and x ^2=8 y i.e. aligned & ( x^2 8 )^2=8 x x (x^3-512 )=0 & O (0,0) and P (8,8) & A= ₀^8(2 2 )( x ) d x- ₀^8 x^2 8 d x & .= 2 2 ( 3 2 ) x^ 3 2 ]₀^8- 1 24 [x^3 ]₀^8= ( 4 2 3 )(8 8 )- 1 24 (512)= 64 3 sq. units aligned

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