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<!DOCTYPE html><html lang="en" data-theme="light"><head><meta charset="UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Hexo</title><meta name="author" content="John Doe"><meta name="copyright" content="John Doe"><meta name="format-detection" content="telephone=no"><meta name="theme-color" content="#ffffff"><meta property="og:type" content="website">
<meta property="og:title" content="Hexo">
<meta property="og:url" content="http://example.com/index.html">
<meta property="og:site_name" content="Hexo">
<meta property="og:locale" content="en_US">
<meta property="og:image" content="https://i.loli.net/2021/02/24/5O1day2nriDzjSu.png">
<meta property="article:author" content="John Doe">
<meta name="twitter:card" content="summary">
<meta name="twitter:image" content="https://i.loli.net/2021/02/24/5O1day2nriDzjSu.png"><link rel="shortcut icon" href="/img/favicon.png"><link rel="canonical" href="http://example.com/"><link rel="preconnect" href="//cdn.jsdelivr.net"/><link rel="preconnect" href="//busuanzi.ibruce.info"/><link rel="stylesheet" href="/css/index.css"><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/@fortawesome/fontawesome-free/css/all.min.css" media="print" onload="this.media='all'"><script>const GLOBAL_CONFIG = {
root: '/',
algolia: undefined,
localSearch: undefined,
translate: undefined,
noticeOutdate: undefined,
highlight: {"plugin":"highlighjs","highlightCopy":true,"highlightLang":true,"highlightHeightLimit":false},
copy: {
success: 'Copy successfully',
error: 'Copy error',
noSupport: 'The browser does not support'
},
relativeDate: {
homepage: false,
post: false
},
runtime: '',
date_suffix: {
just: 'Just',
min: 'minutes ago',
hour: 'hours ago',
day: 'days ago',
month: 'months ago'
},
copyright: undefined,
lightbox: 'fancybox',
Snackbar: undefined,
source: {
jQuery: 'https://cdn.jsdelivr.net/npm/jquery@latest/dist/jquery.min.js',
justifiedGallery: {
js: 'https://cdn.jsdelivr.net/npm/justifiedGallery/dist/js/jquery.justifiedGallery.min.js',
css: 'https://cdn.jsdelivr.net/npm/justifiedGallery/dist/css/justifiedGallery.min.css'
},
fancybox: {
js: 'https://cdn.jsdelivr.net/npm/@fancyapps/fancybox@latest/dist/jquery.fancybox.min.js',
css: 'https://cdn.jsdelivr.net/npm/@fancyapps/fancybox@latest/dist/jquery.fancybox.min.css'
}
},
isPhotoFigcaption: false,
islazyload: false,
isanchor: false
}</script><script id="config-diff">var GLOBAL_CONFIG_SITE = {
title: 'Hexo',
isPost: false,
isHome: true,
isHighlightShrink: false,
isToc: false,
postUpdate: '2021-12-26 15:28:02'
}</script><noscript><style type="text/css">
#nav {
opacity: 1
}
.justified-gallery img {
opacity: 1
}
#recent-posts time,
#post-meta time {
display: inline !important
}
</style></noscript><script>(win=>{
win.saveToLocal = {
set: function setWithExpiry(key, value, ttl) {
if (ttl === 0) return
const now = new Date()
const expiryDay = ttl * 86400000
const item = {
value: value,
expiry: now.getTime() + expiryDay,
}
localStorage.setItem(key, JSON.stringify(item))
},
get: function getWithExpiry(key) {
const itemStr = localStorage.getItem(key)
if (!itemStr) {
return undefined
}
const item = JSON.parse(itemStr)
const now = new Date()
if (now.getTime() > item.expiry) {
localStorage.removeItem(key)
return undefined
}
return item.value
}
}
win.getScript = url => new Promise((resolve, reject) => {
const script = document.createElement('script')
script.src = url
script.async = true
script.onerror = reject
script.onload = script.onreadystatechange = function() {
const loadState = this.readyState
if (loadState && loadState !== 'loaded' && loadState !== 'complete') return
script.onload = script.onreadystatechange = null
resolve()
}
document.head.appendChild(script)
})
win.activateDarkMode = function () {
document.documentElement.setAttribute('data-theme', 'dark')
if (document.querySelector('meta[name="theme-color"]') !== null) {
document.querySelector('meta[name="theme-color"]').setAttribute('content', '#0d0d0d')
}
}
win.activateLightMode = function () {
document.documentElement.setAttribute('data-theme', 'light')
if (document.querySelector('meta[name="theme-color"]') !== null) {
document.querySelector('meta[name="theme-color"]').setAttribute('content', '#ffffff')
}
}
const t = saveToLocal.get('theme')
if (t === 'dark') activateDarkMode()
else if (t === 'light') activateLightMode()
const asideStatus = saveToLocal.get('aside-status')
if (asideStatus !== undefined) {
if (asideStatus === 'hide') {
document.documentElement.classList.add('hide-aside')
} else {
document.documentElement.classList.remove('hide-aside')
}
}
const detectApple = () => {
if (GLOBAL_CONFIG_SITE.isHome && /iPad|iPhone|iPod|Macintosh/.test(navigator.userAgent)){
document.documentElement.classList.add('apple')
}
}
detectApple()
})(window)</script><meta name="generator" content="Hexo 5.4.0"><link rel="alternate" href="/atom.xml" title="Hexo" type="application/atom+xml">
</head><body><div id="sidebar"><div id="menu-mask"></div><div id="sidebar-menus"><div class="avatar-img is-center"><img src="https://i.loli.net/2021/02/24/5O1day2nriDzjSu.png" onerror="onerror=null;src='/img/friend_404.gif'" alt="avatar"/></div><div class="site-data"><div class="data-item is-center"><div class="data-item-link"><a href="/archives/"><div class="headline">Articles</div><div class="length-num">2</div></a></div></div></div><hr/></div></div><div class="page" id="body-wrap"><header class="full_page" id="page-header"><nav id="nav"><span id="blog_name"><a id="site-name" href="/">Hexo</a></span><div id="menus"><div id="toggle-menu"><a class="site-page"><i class="fas fa-bars fa-fw"></i></a></div></div></nav><div id="site-info"><h1 id="site-title">Hexo</h1></div><div id="scroll-down"><i class="fas fa-angle-down scroll-down-effects"></i></div></header><main class="layout" id="content-inner"><div class="recent-posts" id="recent-posts"><div class="recent-post-item"><div class="post_cover left_radius"><a href="/2021/12/26/%E6%95%B0%E5%80%BC%E7%A7%AF%E5%88%86--%E8%87%AA%E9%80%82%E5%BA%94%E8%BE%9B%E6%99%AE%E6%A3%AE%E6%B3%95/" title="No title"> <img class="post_bg" src="https://cdn.jsdelivr.net/npm/butterfly-extsrc@1/img/default.jpg" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="No title"></a></div><div class="recent-post-info"><a class="article-title" href="/2021/12/26/%E6%95%B0%E5%80%BC%E7%A7%AF%E5%88%86--%E8%87%AA%E9%80%82%E5%BA%94%E8%BE%9B%E6%99%AE%E6%A3%AE%E6%B3%95/" title="No title">No title</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">Created</span><time datetime="2021-12-26T06:59:34.216Z" title="Created 2021-12-26 14:59:34">2021-12-26</time></span></div><div class="content">定积分的定义简单来说，函数 $f(x)$ 在区间 $[l,r]$ 上的定积分 $\int_{l}^{r}f(x)\mathrm{d}x$ 指的是 $f(x)$ 在区间 $[l,r]$ 中与 $x$ 轴围成的区域的面积（其中 $x$ 轴上方的部分为正值，$x$ 轴下方的部分为负值）。
很多情况下，我们需要高效，准确地求出一个积分的近似值。下面介绍的 辛普森法，就是这样一种求数值积分的方法。
辛普森法这个方法的思想是将被积区间分为若干小段，每段套用二次函数的积分公式进行计算。 对于一个二次函数 $f(x)=Ax^2+Bx+C$，有：$$\int_l^r f(x) {\mathrm d}x = \frac{(r-l)(f(l)+f(r)+4 f(\frac{l+r}{2}))}{6}$$
推导过程：对于一个二次函数 $f(x)=Ax^2+Bx+C$；求积分可得 $F(x)=\int_0^x f(x) {\mathrm d}x = \frac{a}{3}x^3+\frac{b}{2}x^2+cx+D$ 在这里 D 是一个常数，那么
$$\begin{aligned}\int_l^r f(x ...</div></div></div><div class="recent-post-item"><div class="post_cover right_radius"><a href="/2021/12/26/hello-world/" title="Hello World"> <img class="post_bg" src="https://cdn.jsdelivr.net/npm/butterfly-extsrc@1/img/default.jpg" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="Hello World"></a></div><div class="recent-post-info"><a class="article-title" href="/2021/12/26/hello-world/" title="Hello World">Hello World</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">Created</span><time datetime="2021-12-26T05:48:31.223Z" title="Created 2021-12-26 13:48:31">2021-12-26</time></span></div><div class="content">Welcome to Hexo! This is your very first post. Check documentation for more info. If you get any problems when using Hexo, you can find the answer in troubleshooting or you can ask me on GitHub.
Quick StartCreate a new post1$ hexo new "My New Post"
More info: Writing
Run server1$ hexo server
More info: Server
Generate static files1$ hexo generate
More info: Generating
Deploy to remote sites1$ hexo deploy
More info: Deployment
</div></div></div><nav id="pagination"><div class="pagination"><span class="page-number current">1</span></div></nav></div><div class="aside-content" id="aside-content"><div class="card-widget card-info"><div class="is-center"><div class="avatar-img"><img src="https://i.loli.net/2021/02/24/5O1day2nriDzjSu.png" onerror="this.onerror=null;this.src='/img/friend_404.gif'" alt="avatar"/></div><div class="author-info__name">John Doe</div><div class="author-info__description"></div></div><div class="card-info-data"><div class="card-info-data-item is-center"><a href="/archives/"><div class="headline">Articles</div><div class="length-num">2</div></a></div></div><a class="button--animated" id="card-info-btn" target="_blank" rel="noopener" href="https://github.com/xxxxxx"><i class="fab fa-github"></i><span>Follow Me</span></a></div><div class="card-widget card-announcement"><div class="item-headline"><i class="fas fa-bullhorn card-announcement-animation"></i><span>Announcement</span></div><div class="announcement_content">This is my Blog</div></div><div class="sticky_layout"><div class="card-widget card-recent-post"><div class="item-headline"><i class="fas fa-history"></i><span>Recent Post</span></div><div class="aside-list"><div class="aside-list-item"><a class="thumbnail" href="/2021/12/26/%E6%95%B0%E5%80%BC%E7%A7%AF%E5%88%86--%E8%87%AA%E9%80%82%E5%BA%94%E8%BE%9B%E6%99%AE%E6%A3%AE%E6%B3%95/" title="No title"><img src="https://cdn.jsdelivr.net/npm/butterfly-extsrc@1/img/default.jpg" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="No title"/></a><div class="content"><a class="title" href="/2021/12/26/%E6%95%B0%E5%80%BC%E7%A7%AF%E5%88%86--%E8%87%AA%E9%80%82%E5%BA%94%E8%BE%9B%E6%99%AE%E6%A3%AE%E6%B3%95/" title="No title">No title</a><time datetime="2021-12-26T06:59:34.216Z" title="Created 2021-12-26 14:59:34">2021-12-26</time></div></div><div class="aside-list-item"><a class="thumbnail" href="/2021/12/26/hello-world/" title="Hello World"><img src="https://cdn.jsdelivr.net/npm/butterfly-extsrc@1/img/default.jpg" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="Hello World"/></a><div class="content"><a class="title" href="/2021/12/26/hello-world/" title="Hello World">Hello World</a><time datetime="2021-12-26T05:48:31.223Z" title="Created 2021-12-26 13:48:31">2021-12-26</time></div></div></div></div><div class="card-widget card-archives"><div class="item-headline"><i class="fas fa-archive"></i><span>Archives</span></div><ul class="card-archive-list"><li class="card-archive-list-item"><a class="card-archive-list-link" href="/archives/2021/12/"><span class="card-archive-list-date">December 2021</span><span class="card-archive-list-count">2</span></a></li></ul></div><div class="card-widget card-webinfo"><div class="item-headline"><i class="fas fa-chart-line"></i><span>Info</span></div><div class="webinfo"><div class="webinfo-item"><div class="item-name">Article :</div><div class="item-count">2</div></div><div class="webinfo-item"><div class="item-name">UV :</div><div class="item-count" id="busuanzi_value_site_uv"></div></div><div class="webinfo-item"><div class="item-name">PV :</div><div class="item-count" id="busuanzi_value_site_pv"></div></div><div class="webinfo-item"><div class="item-name">Last Push :</div><div class="item-count" id="last-push-date" data-lastPushDate="2021-12-26T07:28:02.384Z"></div></div></div></div></div></div></main><footer id="footer"><div id="footer-wrap"><div class="copyright">©2020 - 2021 By John Doe</div><div class="framework-info"><span>Framework </span><a target="_blank" rel="noopener" href="https://hexo.io">Hexo</a><span class="footer-separator">|</span><span>Theme </span><a target="_blank" rel="noopener" href="https://github.com/jerryc127/hexo-theme-butterfly">Butterfly</a></div></div></footer></div><div id="rightside"><div id="rightside-config-hide"><button id="darkmode" type="button" title="Switch Between Light And Dark Mode"><i class="fas fa-adjust"></i></button><button id="hide-aside-btn" type="button" title="Toggle between single-column and double-column"><i class="fas fa-arrows-alt-h"></i></button></div><div id="rightside-config-show"><button id="rightside_config" type="button" title="Setting"><i class="fas fa-cog fa-spin"></i></button><button id="go-up" type="button" title="Back To Top"><i class="fas fa-arrow-up"></i></button></div></div><div><script src="/js/utils.js"></script><script src="/js/main.js"></script><div class="js-pjax"></div><script async data-pjax src="//busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script></div></body></html>