The area under a ground-to-ground projectile trajectory between the point of projection and the point of landing is:
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The area under a ground-to-ground projectile trajectory between the point of projection and the point of landing is:

G1 Physics · Accepted Answer

Use y = 4Hx(R−x)/R². Area: A = ∫₀ᴿ y dx = (4H/R²)∫₀ᴿ [Rx−x²]dx = (4H/R²)[R³/2−R³/3] = (4H/R²)(R³/6) = 2RH/3.