[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-572341-105":3,"detail-sidebar-cat-1-en-105":72,"doc-detail-572341-en":118},{"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":65,"head_meta":67,"extra_data":69,"updated_unix":71},105,"en","math-175-common-formula-sheet-read-online-free","Math 175 Common Formula Sheet - read online free","","A compact reference sheet for Math 175 summarizing key calculus and mathematical methods. Covers volume, moment, mass and centers of mass, arc length, surface area, and work. Includes major integration techniques such as integration by parts, trigonometric substitution, and common integration formulas with notes on constants. Also provides numerical approximation rules (trapezoidal and Simpson’s), differential equation solution forms, polar coordinate calculus, and convergence tests plus common series.",{"@graph":14,"@context":64},[15,34,55],{"@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/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/paper-templates/","Paper Templates",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/math-175-common-formula-sheet-read-online-free/572341/",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/math-175-common-formula-sheet-read-online-free/572341.png","ImageObject",442,249,{"name":42,"@type":43},"Maya Linwood","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58],{"name":59,"@type":60,"acceptedAnswer":61},"What approximation rules and differential equation forms are summarized?","Question",{"text":62,"@type":63},"It provides the trapezoidal rule and Simpson’s rule for approximating integrals, and includes separable differential equations plus the first-order linear differential equation form and its solution.","Answer","https://schema.org",{"og:url":32,"og:type":66,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":68,"canonical":32},"index,follow",{"doc_id":70,"site_id":7},572341,1792052363,{"code":4,"msg":73,"data":74},"success",[75,80,85,90,95,100,105,110,114],{"id":76,"doc_module":22,"doc_module_name":25,"category_name":77,"show_sort_weight":78,"slug":79},11,"Presentations",90,"presentations",{"id":81,"doc_module":22,"doc_module_name":25,"category_name":82,"show_sort_weight":83,"slug":84},12,"Resumes",80,"resumes",{"id":86,"doc_module":22,"doc_module_name":25,"category_name":87,"show_sort_weight":88,"slug":89},14,"Invoices",70,"invoices",{"id":91,"doc_module":22,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},15,"Posters",60,"posters",{"id":96,"doc_module":22,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},16,"Social Media",50,"social-media",{"id":101,"doc_module":22,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},17,"Forms",40,"forms",{"id":106,"doc_module":22,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},18,"Letters",30,"letters",{"id":111,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},21,5,"papers-templates",{"id":115,"doc_module":22,"doc_module_name":25,"category_name":116,"show_sort_weight":4,"slug":117},158,"General","general-158",{"code":4,"msg":73,"data":119},{"doc_id":70,"user_id":120,"nickname":42,"user_avatar":121,"doc_module":22,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":122,"file_id":123,"file_url":124,"file_type":125,"file_size":126,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":127,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":128,"faqs":129,"seo_title":130,"seo_description":12,"update_tm":131,"read_time":22},962084928432,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Math 175 Common Formula Sheet  \nVolume Formulas  \nVolume of a solid with cross section 􀜣(􀝔)  \n􀜸 = ∫􀯕􀯔 􀜣 (􀝔)􀝀􀝔 Volume by disk, revolved around x-axis  \n􀜸 = ∫􀯕􀯔 􀟨 [􀜴 (􀝔)]2 􀝀􀝔 Volume by washers, revolved around x-axis  \n􀜸 = ∫􀯕􀯔 􀟨 [􀜴 (􀝔)]2 − 􀟨 [􀝎 (􀝔)]2 􀝀􀝔 Volume by cylindrical shells, revolved about vertical line  \n􀜸 = ∫􀯕􀯔 2􀟨 (rsahdellius) (shellheight) 􀝀􀝔  \nPappus’s Theorem for Volumes (plane region revolved once about a line in the plane)  \n􀜸 = 2􀟨􀟩􀜣  \nMoments and Centers of Mass  \nMoment about the x-axis  \n􀜯􀯫 = ∫ 􀝕̃􀝀􀝉 Moment about the y-axis  \n􀜯􀯬 = ∫ 􀝔̃􀝀􀝉  \nMass  \n􀜯 = ∫ 􀝀􀝉  \nCenter of mass bounded by curves with constant density  \n􀝔̅ = 1􀯆 ∫􀯕􀯔 􀟜􀝔 [􀝂(􀝔) − 􀝃 (􀝔)]􀝀􀝔  \n􀝕̅ = 1􀯆 ∫􀯕􀯔 􀰋2 [(􀝂(􀝔))2 − (􀝃 (􀝔))2 ]􀝀􀝔  \n\n| Arc Length\u003Cbr>Length of the curve given by 􀝕 = 􀝂 (􀝔), from a to b\u003Cbr>􀜮 = ∫􀯕􀯔 √1 + [􀝂′(􀝔)]2 􀝀􀝔 Length of curve defined parametrically |  |\n| --- | --- |\n| 􀜮 = 􀯕 | √ [􀯗􀯗􀯫􀯧]2 + [􀯗􀯗􀯬􀯧]2 􀝀􀝐 |\n\nSurface Area  \nArea of a surface, revolved around x-axis  \n􀜵 = ∫􀯕􀯔 2􀟨􀝂(􀝔)√1 + [􀝂′(􀝔)]2 􀝀􀝔 Pappus’s Theorem for Surface Areas (plane region revolved once about a line in the plane)  \n􀜵 = 2􀟨􀟩􀜮  \nWork  \nWork done by a variable force 􀜨(􀝔), along x-axis  \n􀜹 = ∫􀯕􀯔 􀜨 (􀝔)􀝀􀝔  \nTechniques of integration  \nIntegration by parts  \n∫ 􀝑􀝀􀝒 = 􀝑􀝒 − ∫ 􀝒􀝀􀝑  \nTrigonometric Substitution  \n􀝂􀝋􀝎 √ 􀜽2 − 􀝔 2 􀝑􀝏􀝁 􀝔 = 􀜽􀝏􀝅􀝊􀟠  \n􀝂􀝋􀝎 √ 􀜽2 + 􀝔 2 􀝑􀝏􀝁 􀝔 = 􀜽􀝐􀜽􀝊􀟠  \n􀝂􀝋􀝎 √􀝔 2 − 􀜽 2 􀝑􀝏􀝁 􀝔 = 􀜽􀝏􀝁􀜿􀟠  \nIntegration Formulas (Constants of integration have been omitted)  \n∫ 􀝔 􀯡 􀝀􀝔 = 􀝔􀝊11 􀝂􀝋􀝎 􀝊 ≠ −1 ∫ 1􀝔 􀝀􀝔 = 􀝈􀝊|􀝔|  \n∫ 􀝁 􀯫 􀝀􀝔 = 􀝁 􀯫  \n∫ 􀜽 􀯫 􀝀􀝔 = ln􀜽(􀯫􀜽) 􀝂􀝋􀝎 􀝊 ≠ −1 ∫ 􀝏􀝅􀝊􀝔 􀝀􀝔 = −􀜿􀝋􀝏􀝔∫ 􀜿􀝋􀝏􀝔 􀝀􀝔 = 􀝏􀝅􀝊􀝔  \n∫ 􀝏􀝁􀜿 2 􀝔 􀝀􀝔 = 􀝐􀜽􀝊􀝔∫ 􀜿􀝏􀜿 2 􀝔 􀝀􀝔 = −􀜿􀝋􀝐􀝔∫ 􀝏􀝁􀜿􀝔 􀝐􀜽􀝊􀝔 􀝀􀝔 = sec 􀝔∫ 􀜿􀝏􀜿􀝔 􀜿􀝋􀝐􀝔 􀝀􀝔 = −􀜿􀝏􀜿􀝔∫ 􀝏􀝁􀜿􀝔 􀝀􀝔 = 􀝈􀝊|􀝏􀝁􀜿􀝔 + 􀝐􀜽􀝊􀝔|∫ 􀜿􀝏􀜿􀝔 􀝀􀝔 = 􀝈􀝊|􀜿􀝏􀜿􀝔 − 􀜿􀝋􀝐􀝔|∫ 􀝐􀜽􀝊􀝔 􀝀􀝔 = 􀝈􀝊|􀝏􀝁􀜿􀝔|∫ 􀜿􀝋􀝐􀝔 􀝀􀝔 = 􀝈􀝊|􀝏􀝅􀝊􀝔|  \nApproximating Integrals  \nTrapezoidal Rule 􀯕􀝂 (􀝔)􀝀􀝔 ≈  \n􀜾~~ ~~􀜽 [􀝂(􀝔0) + 2􀝂(􀝔1) + ⋯ + 2􀝂(􀝔􀯡−1) + 􀝂(􀝔􀯡)] Simpson’s Rule  \n􀯕􀝂 (􀝔)􀝀􀝔 ≈  \n􀜾~~ ~~􀜽 [􀝂(􀝔0) + 4􀝂(􀝔1) + 2􀝂(􀝔2) + 4􀝂(􀝔3) ⋯+ 2􀝂(􀝔􀯡−2) + 4􀝂(􀝔􀯡−1) + 􀝂(􀝔􀯡)]  \nDifferential Equations  \nSeparable differential equation Given:  \n􀝀􀝀􀝕􀝔 = 􀝂 (􀝔)􀝃 (􀝕) We can separate and integrate  \n∫ 􀝃~~ ~~1(􀝕) 􀝀􀝕 = ∫ 􀝂 (􀝔)􀝀􀝔 First order linear differential equation Given:  \n􀝀􀝀􀝕􀝔 + 􀜲 (􀝔)􀝕 = 􀜳 (􀝔) The solution is  \n􀝕 = 􀝒~~ ~~1(􀝔) ∫ 􀝒 (􀝔)􀜳 (􀝔)􀝀􀝔 where  \n􀝒 (􀝔) = 􀝁 ∫ 􀯉 (􀯫)􀯗􀯫  \nPolar Coordinate Calculus  \nDerivative  \n􀝀􀝕   􀝂 ′(􀟠) sin 􀟠 + 􀝂(􀟠) cos 􀟠 =  \n􀝀􀝔 􀝂 ′(􀟠) cos (􀟠) − 􀝂(􀟠) sin 􀟠  \nArea under curve  \n􀜣 = 􀰉 ~~ ~~12[􀯙(􀰏)]2 􀯗􀰏 Arc Length  \n􀜮 = 􀰉 √ [􀝂(􀟠)]2 + [􀝂′(􀟠)]2 􀝀􀟠  \nSeries  \nThe ratio test If:  \nl􀯡 |􀜽􀯡􀜽1 | = 􀜮 \u003C 1 Then the series is absolutely convergent  \nThe root test If:  \nlim 􀳙√ |􀜽􀯡 | = 􀜮 \u003C 1 􀯡→∞  \nThen the series is absolutely convergent  \nCommon Series  \nFunction Series Interval of convergence  \n1􀯫~~ ~~ ∑0 􀝔 􀯡 = 1 + 􀝔 + 􀝔 2 + 􀝔 3 + ⋯ (−1, 1)  \n􀝁 􀯫 ∑0 􀯫􀯡􀳙! = 1 + 􀯫1! + 􀯫22! + 􀯫33! + ⋯ (−∞, ∞)  \nsin 􀝔 ∑0 (−1)􀯡 (􀯫22􀯡1)~~ ~~! = 􀝔 − 􀯫33! + 􀯫55! − 􀯫77! + ⋯ (−∞, ∞)  \ncos 􀝔 ∑0 (−1)􀯡 (􀯫22􀳙􀯡)~~ ~~! = 1 − 􀯫22! + 􀯫44! − 􀯫66! + ⋯ (−∞, ∞)􀝈􀝊 (1 + 􀝔) ∑1 (−1)􀯡−1 􀯫􀳙􀯡 = 􀝔 − 􀯫22 + 􀯫33 − 􀯫44 + ⋯ (−1, 1] tan −1 􀝔 ∑0 (−1)􀯡 􀯫2+11 = 􀝔 − 􀯫33 + 􀯫55 − 􀯫77 + ⋯ [−1, 1](1 + 􀝔)􀯠 ∑1 (􀝉􀝊) 􀝔 􀯞 = 1 + 􀝉􀝔 + 􀯠~~ ~~(􀯠!~~ ~~1)􀯫~~ ~~2 + ⋯ (−1, 1)","cbCaibygxFn8Fc1f","https://ap.wps.com/l/cbCaibygxFn8Fc1f","pdf",176527,"English","# Volume Formulas\n## Moments and Centers of Mass\n## Arc Length\n## Surface Area\n## Work\n# Techniques of Integration\n## Integration by Parts\n## Trigonometric Substitution\n## Integration Formulas\n# Approximating Integrals\n## Trapezoidal Rule\n## Simpson’s Rule\n# Differential Equations\n## Separable\n## First Order Linear\n# Polar Coordinate Calculus\n## Derivative\n## Area Under Curve\n## Arc Length\n# Series\n## Ratio Test\n## Root Test\n## Common Series","[{\"question\":\"What approximation rules and differential equation forms are summarized?\",\"answer\":\"It provides the trapezoidal rule and Simpson’s rule for approximating integrals, and includes separable differential equations plus the first-order linear differential equation form and its solution.\"}]","Math 175 Common Formula Sheet - read online free | PDF",1791926851]