



 
La, I know from one of your previous questions that you are studying calculus so I am going to treat this as a calculus problem. I start with a sketch whenever possible. y = 9  x^{2} Archimedes' formula for parabolic arches says that the area under the arch is 2/3 the base times the height. This parabola intersects the xaxis ay x = ± 3 and hence the length of the base is 2 × 3 = 6 units. The height is 9 units so using, Archimedes' formula, the area under the arch is 2/3 × 6 × 9 = 36 square units. To verify that this result is true find the are using integration. For a general parabolic arch modify the steps above for the expression y = a  bx^{2}. Harley  


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