How to calculate leaf area by applying advanced mathematics knowledge

The curve function of leaves is described by regression method, and the area can be calculated by definite integral with curve edge function.

The area of d and a is the area of the trapezoid of the curve (p/6) by subtracting the tangent from the integral of the curve px^3 in [0, 1], and the x axis, x = 1.

S=4∫∫(xy/a)dxdy

=(4/a)[∫(0->； π/2)dθ][∫(0-& gt； a)(r^3sinθcosθ)dr

=a^3/2

Extended data:

General theorem

Theorem 1: If f(x) is continuous in the interval [a, b], then f(x) is integrable in [a, b].

Theorem 2: If the interval f(x) is bounded on [a, b] and there are only finite discontinuous points, then f(x) is integrable on [a, b].

Theorem 3: Let f(x) be monotone in the interval [a, b], then f(x) can be integrated in [a, b].

Definite integral and indefinite integral seem to have nothing to do, but they are closely related in essence because of the support of a mathematically important theory. It seems impossible to subdivide a graph infinitely and then accumulate it, but because of this theory, it can be transformed into calculating integral.

Baidu encyclopedia-definite integral