O A B C is a unit square where O is the origin and B=(1,1) . The curves y^2=x and x^2=y divide the area of the square into three parts O A B O, O B O and O B C O . If a₁, a₂, a₃ are the areas (in sq units) of these parts respectively, then

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O A B C is a unit square where O is the origin and B=(1,1) . The curves y^2=x and x^2=y divide the area of the square into three parts O A B O, O B O and O B C O . If a₁, a₂, a₃ are the areas (in sq units) of these parts respectively, then a₁+2 a₂+3 a₃=

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Correct answer: B. 2

Now, aligned a₂ & = ₀^1 ( x -x^2 ) d x & = [ 2 3 x^ 3 / 2 - x^3 3 ]₀^1= 2 3 - 1 3 = 1 3 aligned So, a₁+a₃+ 1 3 =1 From Eqs. (ii) and (iii), a₁=a₃= 1 3 =a₂ So, a₁+2 a₂+3 a₃= 1 3 + 2 3 + 3 3 =2

O A B C is a unit square where O is the origin and B=(1,1) . The curves y^2=x and x^2=y divide the area of the square into three parts O A B O, O B O and O B C O . If a₁, a₂, a₃ are the areas (in sq units) of these parts respectively, then a₁+2 a₂+3 a₃=

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