Woopydalan said:energy times time isn't an insignificant dimension.
help1please said:Just a question on dimensional analysis here.
I believe that when an integral is taken with respect to time for instance, dt appears as a dummy variable yes? Imagine we had
[tex]\int E\ dt[/tex]
Does this have dimensions of energy times time? Or doesn't the dummy variable count?
Woopydalan said:energy times time isn't an insignificant dimension.
The dimensions of an integral are determined by the number of independent variables in the function being integrated. For example, a single-variable integral will have one dimension, while a double integral will have two dimensions.
The dimensions of an integral are directly related to the number of integrals being evaluated. Each integral adds one dimension to the overall dimension of the integral.
Yes, an integral can have any number of dimensions, depending on the function being integrated. However, it becomes increasingly difficult to visualize and calculate integrals with more than three dimensions.
The dimensions of an integral are important because they determine the type of integral being evaluated and the methods used to solve it. Different dimensions require different techniques and approaches to integration.
The dimensions of an integral determine the number of limits of integration needed. For example, a single-variable integral will have one limit, while a double integral will have two limits.