[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522915-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-522915-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","riemann-sum-tables-problem-set-left-hand-and-right-hand-riemann-sums","Riemann Sum Tables - Problem Set - Left-Hand and Right-Hand Riemann Sums","","Riemann Sum Tables worksheet for Infinite Calculus problems. Students approximate definite integrals by constructing left-hand and right-hand Riemann sums using given x- and f(x)-value tables, and optionally use a provided graph to sketch the function and the resulting sums. The sheet includes four left-hand integral tasks over intervals from 0 to 10 or 14 or 19, followed by four corresponding right-hand tasks using similar tabulated function values.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/riemann-sum-tables-problem-set-left-hand-and-right-hand-riemann-sums/522915/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/riemann-sum-tables-problem-set-left-hand-and-right-hand-riemann-sums/522915.png","ImageObject",300,407,{"name":42,"@type":43},"นรินทร์","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",10,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you approximate the integrals in this worksheet?","Question",{"text":63,"@type":64},"Use the left-hand or right-hand Riemann sum rule with the provided table values for x and f(x) to approximate each definite integral.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What role do the tables of x and f(x) play?",{"text":68,"@type":64},"They provide the sample points and function heights needed to form each rectangle sum for the Riemann approximation.",{"name":70,"@type":61,"acceptedAnswer":71},"Can you use the graph when solving these problems?",{"text":72,"@type":64},"Yes. The worksheet suggests using the provided graph to sketch the function data and the Riemann sums to help visualize the approximation.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522915,1791490425,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":55,"slug":125},"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":96,"preview_page_count":4},2336475104957,"https://ap-avatar.wpscdn.com/avatar/22000c4c6bd8a5076e1?x-image-process=image/resize,m_fixed,w_180,h_180&k=1787554080175789136","Kuta Software-Infinite Calculus Name   \nRiemann Sum Tables Date  Period   \nFor each problem, use a left-hand Riemann sum to approximate the integral based off of the values in the table. You may use the provided graph to sketch the function data and Riemann sums.  \n1) ∫010 f (x) dx  \n\n| x | 0 | 2 | 5 | 7 | 10 |\n| --- | --- | --- | --- | --- | --- |\n| f (x) | 2 | 3 | 5 | 7 | 8 |\n\n2) ∫010 f (x) dx  \n\n| x | 0 | 4 | 6 | 7 | 10 |\n| --- | --- | --- | --- | --- | --- |\n| f (x) | 5 | 3 | 2 | 3 | 5 |\n\nFor each problem, use a right-hand Riemann sum to approximate the integral based off of the values in the table. You may use the provided graph to sketch the function data and Riemann sums.  \n3) ∫014 f (x) dx  \n\n| x | 0 | 3 | 5 | 9 | 13 | 14 |\n| --- | --- | --- | --- | --- | --- | --- |\n| f (x) | −1 | −2 | −1 | 0 | −1 | 0 |\n\n f(x)  \n1  \n0.5  \n−0.5  \n−1  \n−1.5  \n−2  \n−2.5  \n−3  \n2  \n4  \n6  \n8  \n10  \n12  \n14  \nx  \n4) ∫019 f (x) dx  \n\n| x | 0 | 4 | 9 | 10 | 12 | 19 |\n| --- | --- | --- | --- | --- | --- | --- |\n| f (x) | −3 | −5 | −4 | −2 | −1 | 1 |\n\n f(x)  \n2  \n1  \n−1  \n−2  \n−3  \n−4  \n−5  \n−6  \n2 4 6 8 10 12 14 16 18 x  \nKuta Software-Infinite Calculus Name   \nRiemann Sum Tables Date  Period   \nFor each problem, use a left-hand Riemann sum to approximate the integral based off of the values in the table. You may use the provided graph to sketch the function data and Riemann sums.  \n1) ∫010 f (x) dx  \n\n| x | 0 | 2 | 5 | 7 | 10 |\n| --- | --- | --- | --- | --- | --- |\n| f (x) | 2 | 3 | 5 | 7 | 8 |\n\n−1  \n−1  \n1  \n2  \n3  \n4  \n5  \n6  \n7  \n8  \n9  \n10  \nx  \n44  \n2) ∫010 f (x) dx  \n\n| x | 0 | 4 | 6 | 7 | 10 |\n| --- | --- | --- | --- | --- | --- |\n| f (x) | 5 | 3 | 2 | 3 | 5 |\n\n37  \nFor each problem, use a right-hand Riemann sum to approximate the integral based off of the values in the table. You may use the provided graph to sketch the function data and Riemann sums.  \n3) ∫014 f (x) dx  \n\n| x | 0 | 3 | 5 | 9 | 13 | 14 |\n| --- | --- | --- | --- | --- | --- | --- |\n| f (x) | −1 | −2 | −1 | 0 | −1 | 0 |\n\n−12  \n4) ∫019 f (x) dx  \n\n| x | 0 | 4 | 9 | 10 | 12 | 19 |\n| --- | --- | --- | --- | --- | --- | --- |\n| f (x) | −3 | −5 | −4 | −2 | −1 | 1 |\n\n−37  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaialN4W9tiyVq","https://ap.wps.com/l/cbCaialN4W9tiyVq","pdf",60162,"English","# Left-hand Riemann sum problems\n## Problem 1: ∫_0^10 f(x) dx\n## Problem 2: ∫_0^10 f(x) dx\n## Problem 3: ∫_0^14 f(x) dx\n## Problem 4: ∫_0^19 f(x) dx\n# Right-hand Riemann sum problems\n## Problem 3: ∫_0^14 f(x) dx\n## Problem 4: ∫_0^19 f(x) dx","[{\"question\":\"How do you approximate the integrals in this worksheet?\",\"answer\":\"Use the left-hand or right-hand Riemann sum rule with the provided table values for x and f(x) to approximate each definite integral.\"},{\"question\":\"What role do the tables of x and f(x) play?\",\"answer\":\"They provide the sample points and function heights needed to form each rectangle sum for the Riemann approximation.\"},{\"question\":\"Can you use the graph when solving these problems?\",\"answer\":\"Yes. The worksheet suggests using the provided graph to sketch the function data and the Riemann sums to help visualize the approximation.\"}]","Riemann Sum Tables - Problem Set - Left-Hand and Right-Hand Riemann Sums | PDF",1791426303]