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NDA2018MathematicsArea Under CurvesActual

What is the area of the region bounded by the parabolas y^2=6(x-1) and y^2=3 x ?

Options

  1. A6 3
  2. B2 6 3
  3. C4 6 3
  4. D5 6 3

Correct answer

C. 4 6 3

Step-by-step solution

Given parabolas are y^2=6(x-1) .(1) and y^2=3 x ....(2) aligned & y^2=6(x-1) & 6 x-6=y^2 & x= y^2+6 6 = y^2 6 +1 aligned Also, y ^2=3 x x = y ^2 3 . Solving (1), (2), 3 x =6( x -1) 3 x =6 x -6 3 x =6 x =2 . y^2=6 y= 6 . Area aligned & = _ - 6 ^ 6 ( y^2 6 +1- y^2 3 ) d y=2 ₀^ 6 (1- y^2 6 ) d y=2 [y- y^3 18 ]₀^ 6 & =2 [ 6 - ( 6 )^3 18 ]=2 2 6 3 = 4 6 3 aligned

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