{"id":115505,"date":"2022-02-25T15:14:57","date_gmt":"2022-02-25T21:14:57","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=115505"},"modified":"2026-03-28T11:51:07","modified_gmt":"2026-03-28T16:51:07","slug":"left-and-right-riemann-sums","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/left-and-right-riemann-sums\/","title":{"rendered":"Left and Right Riemann Sums"},"content":{"rendered":"<h1>Left and Right Riemann Sums<\/h1>\n\n\t\t\t<div id=\"mmDeferVideoEncompass_XpB6J6BO8TQ\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/png\">\n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_XpB6J6BO8TQ\" data-source-video-id=\"XpB6J6BO8TQ\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Left and Right Riemann Sums Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title=\"Left and Right Riemann Sums\" style=\"background-size:contain;background-image:url(&quot;https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/1773-thumb-final-2.webp&quot;);\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>#videoThumbnailImage_XpB6J6BO8TQ:hover {cursor:pointer;}<\/style>\n\t\t\t<script defer>\n\t\t\t(function (config) {\n\t\t\t\t\"use strict\";\n\t\t\t\tvar thumbnail = document.getElementById(config.thumbnailId);\n\t\t\t\tvar container = document.getElementById(config.containerId);\n\t\t\t\tif (!thumbnail || !container) { return; }\n\n\t\t\t\tthumbnail.addEventListener(\"click\", function () {\n\t\t\t\t\tvar videoId = thumbnail.getAttribute(\"data-source-video-id\");\n\t\t\t\t\tif (!\/^[A-Za-z0-9_-]{11}$\/.test(videoId)) { return; }\n\n\t\t\t\t\tvar iframe = document.createElement(\"iframe\");\n\t\t\t\t\tiframe.id = \"yt\" + videoId;\n\t\t\t\t\tiframe.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\t\tiframe.frameBorder = \"0\";\n\t\t\t\t\tiframe.allow = \"autoplay; fullscreen\";\n\t\t\t\t\tiframe.width = thumbnail.width;\n\t\t\t\t\tiframe.height = thumbnail.height;\n\t\t\t\t\tiframe.setAttribute(\"data-matomo-title\", config.pageTitle);\n\n\t\t\t\t\tvar help = document.createElement(\"div\");\n\t\t\t\t\thelp.id = config.messageId;\n\t\t\t\t\thelp.style.cssText = \"display:none;position:absolute;top:-24px;width:100%;text-align:center;\";\n\t\t\t\t\tvar helpText = document.createElement(\"span\");\n\t\t\t\t\thelpText.style.cssText = \"font-style:italic;font-size:small;border-top:1px solid #fc0;\";\n\t\t\t\t\thelpText.appendChild(document.createTextNode(\"Having trouble? \"));\n\t\t\t\t\tvar helpLink = document.createElement(\"a\");\n\t\t\t\t\thelpLink.href = \"https:\/\/www.youtube.com\/watch?v=\" + encodeURIComponent(videoId);\n\t\t\t\t\thelpLink.target = \"_blank\";\n\t\t\t\t\thelpLink.rel = \"noopener noreferrer\";\n\t\t\t\t\thelpLink.textContent = \"Click here to watch on YouTube.\";\n\t\t\t\t\thelpText.appendChild(helpLink);\n\t\t\t\t\thelp.appendChild(helpText);\n\n\t\t\t\t\tcontainer.replaceChildren(iframe);\n\t\t\t\t\tcontainer.prepend(help);\n\t\t\t\t\tsetTimeout(function () { help.style.display = \"block\"; }, 2000);\n\t\t\t\t});\n\t\t\t})({\"containerId\":\"mmDeferVideoEncompass_XpB6J6BO8TQ\",\"thumbnailId\":\"videoThumbnailImage_XpB6J6BO8TQ\",\"messageId\":\"mmDeferVideoYTMessage_XpB6J6BO8TQ\",\"pageTitle\":\"Left and Right Riemann Sums\"});\n\t\t\t<\/script>\n\t\t\n\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/calculus\/\"><strong>Return to Calculus Videos<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Left and Right Riemann Sums &nbsp; Return to Calculus Videos<\/p>\n","protected":false},"author":22,"featured_media":115508,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":{"0":"post-115505","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-calculus-videos","7":"page_category-video-pages-for-study-course-sidebar-ad","8":"page_type-video","9":"subject_matter-math"},"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 5.0.4 - aioseo.com -->\n\t<meta name=\"description\" content=\"Left and right Riemann sums are methods used to determine the area lying beneath a curve. 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