How much red?
How much red?
We would like our notion of amount (that we're going to call the "integral") to have the
following properties:
amount(
)= 2 times
amount(
)
amount(
)
= half of amount()
amount(
)
= 0
These would all be true if, for a uniform image of redness r,
amount()
= r times area(
)
The notion of amount called the "integral" and defined as the limit
of Riemann sums, is based on this last property, and gives sensible
answers for uniform and non-uniform images:
integral() = 1
integral() = 2
integral() = 0.5
integral() = 0
integral(
) = 8/27 = .296...