Let L = 4x- 5y, L(i) = (x)/(10) - (i)/(n...

Let `L = 4x- 5y, L_(i) = (x)/(10) - (i)/(n), L_(i) = x/10 + y/8 + i/n`, and `E = (x^(2))/(50) + (y^(2))/(32) - 1`. Let`A_(i)` repersents the area of region common between `L_(i-1) gt 0, L_(i) lt 0, E lt 0` and `L lt 0`, `A'_(i)` represents the area of region common between `L'_(i-1) lt 0, L'_(i) gt 0, E lt 0` and `L lt 0`. `B_(i)` repersents the area of region common between `L_(i-1) gt 0, L_(i) lt 0, E lt 0` and `L gt 0`, `B'_(i)` repersents the area of region common between `L'_(i - 1) lt , L'_(i) gt 0, E lt 0` and `L gt 0`, then value of `(A_(1) + A'_(2) + A_(3) + A'_(4) + ".......") + (B_(1) + B'_(2) + B'_(4) + ".......")` is equal to .

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The correct Answer is:

`20 pi`

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