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Challenge 350: Trapezium Trial

The parabola with equation y = 4 – x2 intersects the positive x-axis at Q and the y-axis at P.

The straight line L1 has gradient m and passes through P, and the straight line L2 which passes through Q, is parallel to L1.

L1 intersects the parabola at S and L2 intersects the parabola at R.

Given that m > 0, find an expression for the area of the trapezium PQRS in terms of m.

What if m < 0?