curve = x - 2 Sqrt[x] + y^2 == 0
For this curve, how can we calculate its area and perimeter?
area = 2 Integrate[Sqrt[2 Sqrt[x] - x], {x, 0, 4}]
Is the area-finding method shown above correct? What other methods can be used to calculate the area? How can its perimeter be solved with code?
Thank you very much! The problem has been solved.
I would consider this other way:
func = x - 2 Sqrt[x] + y^2; ContourPlot[func == 0, {x, 0, 5}, {y, -2, 2}] RegionMeasure[ImplicitRegion[func == 0, {x, y}]] RegionPlot[func <= 0, {x, 0, 5}, {y, -2, 2}] Area[ImplicitRegion[func <= 0, {x, y}]]
