The plate R in Figure 8, bounded by the parabola y = x² and y = 1, is submerged vertically in water (distance in meters).

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(a) Show that the width of R at height y is f(y) = 2√y and the fluid force on a side of a horizontal strip of thickness Ay at height y is approximately (pg)2y¹/2(1-y)Ay. (b) Write a Riemann Sum that approximates the fluid force F on a side of R and use it to explain why f₁2y¹/² (1-1) dy (c) Calculate F. 1-y -1 F = pg R 1 f(y) Water surface y=x² ++ √ 1