Find the exact area (in units2) of the region bounded by the given equations if possible. If you are unable to determine the intersection points analytically, use a calculator to approximate the intersection points with three decimal places and determine the approximate area (in units2) of the region, then round your answer to three decimal places.x^2 = y^3 and x = 2y

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12-12-2022
Mathematics

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Find the exact area (in units2) of the region bounded by the given equations if possible. If you are unable to determine the intersection points analytically, use a calculator to approximate the intersection points with three decimal places and determine the approximate area (in units2) of the region, then round your answer to three decimal places.x^2 = y^3 and x = 2y

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contexto1028 contexto1028 · Answer 1 · 2022-12-19T05:47:18-05:00

The region bounded by the equations has a precise area of 21.33 units.

A boundary or some set of constraints are imposed on a bounded region. To put it another way, the size of a bounded shape cannot be infinite. Anything that is bound must be able to be contained within certain parameters.

x2 = 4y2 from equation (1), y3 = 4y2 y3 - 4y2 = 0 y2(y - 4) = 0 y2 = 0 or y-4 = 0 or y = 4 These will be our integration bounds. We have given that x2 = y3 --------- (1) and x = 2y --------- (2).

Therefore, we will express area as A = [- 4]04 = [- 4 - 0] = 64 - 85.33 A = -21.33, or A = 21.33. This indicates that the area of the bounded region is 21.33 units.

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