- #1
chwala
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- Homework Statement
- See attached
- Relevant Equations
- Parametric equations
My question is on how did they determine the limits of integration i.e ##2## and ##3## as highlighted? Thanks
I agree. The graph of the parametric curve ##x = t^2, y = t^3## lies in Quadrants I and IV, and is unbounded. There has to be additional but unstated constraints for the limits of integration that are shown.Frabjous said:I meant that the problem statement did not include the limits, i.e., poorly written.
@WWGD This is not my working rather notes that i came across as indicated by the given internet link;WWGD said:@chwala : It seems in your square root, you're using ##\frac {dx}{dt} ##twice, rather than what I believe is correct, ##\frac {dx}{dt}, \frac{dy}{dt}##
To find the surface area of a rectangular prism, you need to calculate the area of all six faces and then sum them up. The formula is: Surface Area = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.
The surface area of a cylinder can be found using the formula: Surface Area = 2πr(h + r), where r is the radius of the base and h is the height of the cylinder. This formula accounts for the areas of the two circular bases and the rectangular side that wraps around the cylinder.
The surface area of a sphere is calculated using the formula: Surface Area = 4πr², where r is the radius of the sphere. This formula gives you the total area covering the surface of the sphere.
To find the surface area of a cone, you use the formula: Surface Area = πr(r + l), where r is the radius of the base and l is the slant height of the cone. This formula includes the area of the circular base and the lateral surface area.
The surface area of a triangular prism is found by calculating the area of the two triangular bases and the three rectangular faces, then summing these areas. The general formula is: Surface Area = (Base Area x 2) + (Perimeter of Base x Height), where the Base Area is the area of one triangular base, and the Height is the distance between the two triangular bases.