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(1) What is integration
please refer to definition of integration that I do not go through in details. Good question but I do not try to explain true or not true as it is relating to concept and application. (2) Strictly speaking integrate 2πX = πx^2 + constant. So
do you still think integrate 圆周 得出 圆面积 ? (3) integrate 圆面积 会得出什么呢 = relating to volume . Recall result of integration or differentiation on polynomial d/dx ( x^n ) = nX^(n-1)
so Integrate X^(n-1) = x^n / n + c
c is constant For Sphere
when volume
area
perimeter
are respectively represented by equations V=4/3 pi x^3
where x=radius
A= pi x^2
L = 2 pi X obviously
it has already set the relation of V
A
and L by X. so
when you applying integration on L
result will be relating to A
when applying integration to A
result will be relating to V. you can cite another example of a solid cube of volume V
area A and edge length L respectively by formula V= X^3 A=6X^2 where A is surface area L=X pls apply integrate or differentiation to V
A
L respective X
sure it shows some relationship of the result because already pre-set relation of V
A and L. Hope it is clear.
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