第四十六章 计算(2 / 2)

“再代入别的数字,x=2,原函数答案是4,y=2x围成的面积是,2×4÷2=4,也等于4。”

“下面的以此类推,答案完全一样。”

“甚至就是算梯形的面积,其实也是一样的。”

李纵用一个很巧合的例子,来说明在给定边界后,的确可以通过原函数的式子来算出图形的面积。并且计算出来的面积是完全吻合的,这恰恰印证了前面李纵的假设。

虽说这只是个例,但是,此法足以让两人耳目一新。

三角形的面积原来还能这么算,这谁能想到!

然后李纵便道:“其实还有更为严格的证明过程,只是便于你们好理解,我也就拿这个作为例子。”

“假设这就是对的!”

“那么,以前我们是不是写了一条关于圆的方程的式子,是不是也有xy,而且当时我们还算出了边界,如果我没有记错的话,是b点的坐标是四分之一。”

“要是我们也能知道那条圆的方程的式子的原函数,是不是就能够通过直接代入四分之一,当然,起点是0,所以不用算,去算那个小区域S(ABD)的面积。”

两人听完,简直觉得李纵就是鬼才!

这都能让李纵想到!

但是……

接下来,等李纵把圆的方程式子写下来后,这个要怎么求原函数,却是把所有人都难倒了。

“这个式子,要怎么求原函数。”

“方才,我们是瞎猫碰上死耗子,正好通过微分,算出来是2x,那么接下来什么原函数的微分等于(x-x),再开根号。”

张公绰两人立刻都傻眼了。

甚至,看完了这条式子,前面什么微分、积分好像都忘了,这就是所谓的,你看完,你觉得你自己懂了,其实,你什么都不懂。(图)

“这的确是一条相当复杂的式子,而且微分的过程虽说我们从头到尾都是知道的,但是我们却又不可能从后面往前推。”

“尤其还是这种又有减法,甚至还有开平方的式子。”

“这怎么办?”

“我们化简一下。”

“这就是结果。”

“然后我们先不管前面的x的二分之一方,我们就看后面的这个,(1-x)的二分之一方,是不是就跟我们之前提到的,那个f(m)的公式长得很像。”

“那我们是不是就可以把这个式子,按照f(m)的式子来展开。”

“最后得到。”

“我们再对这个式子求原函数。”

<--di--!>
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