Calculate from a parabolic building?

Question

Hello, how do you calculate the surface area of ​​a parabolic building?

guteantwort2021 · Answer

Hello. Form the master function and calculate integral between the two zeros. At least my guess without task or sketch. 😋 LG

halbrecht · Answer

One would have to determine the length of the parabolic arch with a so-called curved integral.

for illustration:

From -1.5 to +1.5 is the parabola

5.65264 units long

.

PS The principle is similar to the jacket of a cylinder.

Source of the picture

seifenkistenbob · Answer

If the arc length L of the functional graph of the downwardly opened parabola is known in the searched section, it can easily be calculated if we assume that the building consists of the following areas:

a base surface with the side lengths a and b (G=a*b)
two side surfaces with the parabola-shaped cross section (opened at the bottom) and the maximum side length a (can easily be determined by integration)
a roof whose surface area D consists of the arc length L and the other side of the base area (D=L*b)

If the arc length is not known but only a function definition is present, it can be calculated via a line integral (also: curve/way integral).

The arc length can also be graphically approached by drawing points on the graph in small intervals, connecting them to one another and measuring their length, or calculating them by Pythagoras. Depending on the number of points (ie accuracy), this is very laborious with pen and paper.

The integral for the path length does nothing else, but only for infinite small intervals:

The path length L with the path X is then calculated in this way: