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?
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}]]
Thank you very much! The problem has been solved.
