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Problems guide the student to use 4 left-endpoint rectangles for two functions over specified intervals, then 5 right-endpoint rectangles for two additional functions. Further tasks use 4 inscribed rectangles and 4 midpoint rectangles, with each exercise providing a function and an interval for computation. Graph sketching is suggested to visualize the rectangles under the curve.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/approximating-area-under-a-curve-worksheet-06-approximating-area-under-a-curve/522901/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/approximating-area-under-a-curve-worksheet-06-approximating-area-under-a-curve/522901.png","ImageObject",300,407,{"name":92,"@type":93},"วิน","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the worksheet ask you to approximate in each problem?","Question",{"text":112,"@type":113},"It asks you to approximate the area under the given curve over the provided interval.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which rectangle method is used for the first set of problems?",{"text":117,"@type":113},"The first problems use 4 left endpoint rectangles.",{"name":119,"@type":110,"acceptedAnswer":120},"What rectangle method is used in the last problems on the worksheet?",{"text":121,"@type":113},"The worksheet uses 4 midpoint rectangles for the final set of functions.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522901,1791766098,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},2336475104736,"https://ap-avatar.wpscdn.com/avatar/22000c4c5e0e5b17e70?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786591360781797222","Kuta Software-Infinite Calculus Name   \nApproximating Area Under a Curve Date  Period   \nFor each problem, approximate the area under the curve over the given interval using 4 left endpoint  \nrectangles.  \n2  \n1) y = x2~~ ~~ + x + 2; [−5, 3]  \n2) y = x 2 + 3; [−3, 1]  \nFor each problem, approximate the area under the curve over the given interval using 5 right endpoint rectangles. You may use the provided graph to sketch the curve and rectangles.  \n2  \n3) y = − ~~ ~~x2~~ ~~ + 6; [−3, 2]  \n2  \n4) y = − ~~ ~~x2~~ ~~ + x + 5; [−1, 4]  \nFor each problem, approximate the area under the curve over the given interval using 4 inscribed rectangles. You may use the provided graph to sketch the curve and rectangles.  \n5) y = −x + 5; [−7, −5]  \n6) y = 2x~~ ~~ ; [1, 5]  \nFor each problem, approximate the area under the curve over the given interval using 4 midpoint rectangles. You may use the provided graph to sketch the curve and rectangles.  \n7) y = − x 2 + 2x + 11; [−1, 3]  \n8) y = x 2 − 2x + 3; [−1, 3]  \nKuta Software-Infinite Calculus Name   \nApproximating Area Under a Curve Date  Period   \nFor each problem, approximate the area under the curve over the given interval using 4 left endpoint  \nrectangles.  \n2  \n1) y = x2~~ ~~ + x + 2; [−5, 3]  \n36  \n2) y = x 2 + 3; [−3, 1]  \n26  \nFor each problem, approximate the area under the curve over the given interval using 5 right endpoint rectangles. You may use the provided graph to sketch the curve and rectangles.  \n2  \n3) y = − ~~ ~~x2~~ ~~ + 6; [−3, 2]  \n25  \n2  \n4) y = − ~~ ~~x2~~ ~~ + x + 5; [−1, 4]  \n20  \nFor each problem, approximate the area under the curve over the given interval using 4 inscribed rectangles. You may use the provided graph to sketch the curve and rectangles.  \n5) y = −x + 5; [−7, −5]  \n432 = 21.5  \nFor each problem, approximate the area under the curve over the given interval using 4 midpoint rectangles. You may use the provided graph to sketch the curve and rectangles.  \n7) y = − x 2 + 2x + 11; [−1, 3]  \n43  \n8) y = x 2 − 2x + 3; [−1, 3]  \n13  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaioOaxHVEJsbP","https://ap.wps.com/l/cbCaioOaxHVEJsbP","pdf",97351,"English","# Approximating Area Under a Curve\n## 4 Left Endpoint Rectangles\n## 5 Right Endpoint Rectangles\n## 4 Inscribed Rectangles\n## 4 Midpoint Rectangles","[{\"question\":\"What does the worksheet ask you to approximate in each problem?\",\"answer\":\"It asks you to approximate the area under the given curve over the provided interval.\"},{\"question\":\"Which rectangle method is used for the first set of problems?\",\"answer\":\"The first problems use 4 left endpoint rectangles.\"},{\"question\":\"What rectangle method is used in the last problems on the worksheet?\",\"answer\":\"The worksheet uses 4 midpoint rectangles for the final set of functions.\"}]","Approximating Area Under a Curve - Worksheet 06 - Approximating Area Under a Curve | PDF",1791426290]