{"id":8386,"date":"2021-11-21T00:41:38","date_gmt":"2021-11-20T19:11:38","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8386"},"modified":"2021-11-21T01:13:02","modified_gmt":"2021-11-20T19:43:02","slug":"what-is-wallis-formula-in-integration","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/","title":{"rendered":"What is walli’s formula in integration ?"},"content":{"rendered":"

Walli’s Formula :<\/h2>\n

If m,n \\(\\in\\) N & m, n \\(\\ge\\) 2, then<\/p>\n

\n

(a)  \\(\\int_{0}^{\\pi\/2}\\) \\(sin^nx\\)dx = \\(\\int_{0}^{\\pi\/2}\\) \\(cos^nx\\)dx = \\((n-1)(n-3)….(1 or 2)\\over {n(n-2)….(1 or 2)}\\) K<\/p>\n

where K = \\(\\begin{cases} \\pi\/2 & \\text{if n is even}\\ \\\\ 1 & \\text{if n is odd}\\ \\end{cases}\\)<\/p>\n

(b)  \\(sin^nx.cos^mx\\)dx = \\([(n-1)(n-3)….(1 or 2)][(m-1)(m-3)….(1 or 2)]\\over {(m+n)(m+n-2)(m+n-4)….(1 or 2)}\\) K<\/p>\n

where K = \\(\\begin{cases} \\pi\/2 & \\text{if both m and n are even}\\ \\\\ 1 & \\text{otherwise}\\ \\end{cases}\\).<\/p>\n<\/blockquote>\n

Example<\/strong><\/span> : Evaluate : \\(\\int_{-\\pi\/2}^{\\pi\/2}\\) \\(sin^4x cos^6x\\)dx<\/p>\n

Solution<\/strong><\/span> : We have,<\/p>\n

I = \\(\\int_{-\\pi\/2}^{\\pi\/2}\\) \\(sin^4x cos^6x\\)dx = 2 \\(\\int_{0}^{\\pi\/2}\\) \\(sin^4x cos^6x\\)dx <\/p>\n

I = 2\\((3.1)(5.3.1)\\over 10.8.6.4.2\\) \\(\\pi\\over 2\\) = \\(3\\pi\\over 6\\)<\/p>\n\n\n

\n
Previous – Newton Leibnitz formula with Examples<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Walli’s Formula : If m,n \\(\\in\\) N & m, n \\(\\ge\\) 2, then (a)  \\(\\int_{0}^{\\pi\/2}\\) \\(sin^nx\\)dx = \\(\\int_{0}^{\\pi\/2}\\) \\(cos^nx\\)dx = \\((n-1)(n-3)….(1 or 2)\\over {n(n-2)….(1 or 2)}\\) K where K = \\(\\begin{cases} \\pi\/2 & \\text{if n is even}\\ \\\\ 1 & \\text{if n is odd}\\ \\end{cases}\\) (b)  \\(sin^nx.cos^mx\\)dx = \\([(n-1)(n-3)….(1 or 2)][(m-1)(m-3)….(1 or 2)]\\over {(m+n)(m+n-2)(m+n-4)….(1 or …<\/p>\n

What is walli’s formula in integration ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[31],"tags":[204,205,206],"yoast_head":"\nWhat is walli's formula in integration ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is walli's formula for sine and cosine function in definite integration with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is walli's formula in integration ? - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn what is walli's formula for sine and cosine function in definite integration with examples.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-11-20T19:11:38+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-20T19:43:02+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"What is walli’s formula in integration ?\",\"datePublished\":\"2021-11-20T19:11:38+00:00\",\"dateModified\":\"2021-11-20T19:43:02+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/\"},\"wordCount\":143,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"integration\",\"walli's formula\",\"wallis formula example\"],\"articleSection\":[\"Definite Integration\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/\",\"url\":\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/\",\"name\":\"What is walli's formula in integration ? - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-11-20T19:11:38+00:00\",\"dateModified\":\"2021-11-20T19:43:02+00:00\",\"description\":\"In this post you will learn what is walli's formula for sine and cosine function in definite integration with examples.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"What is walli’s formula in integration ?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"What is walli's formula in integration ? - Mathemerize","description":"In this post you will learn what is walli's formula for sine and cosine function in definite integration with examples.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/","og_locale":"en_US","og_type":"article","og_title":"What is walli's formula in integration ? - Mathemerize","og_description":"In this post you will learn what is walli's formula for sine and cosine function in definite integration with examples.","og_url":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/","og_site_name":"Mathemerize","article_published_time":"2021-11-20T19:11:38+00:00","article_modified_time":"2021-11-20T19:43:02+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"What is walli’s formula in integration ?","datePublished":"2021-11-20T19:11:38+00:00","dateModified":"2021-11-20T19:43:02+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/"},"wordCount":143,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"keywords":["integration","walli's formula","wallis formula example"],"articleSection":["Definite Integration"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/","url":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/","name":"What is walli's formula in integration ? - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-11-20T19:11:38+00:00","dateModified":"2021-11-20T19:43:02+00:00","description":"In this post you will learn what is walli's formula for sine and cosine function in definite integration with examples.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/what-is-wallis-formula-in-integration\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"What is walli’s formula in integration ?"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/8386"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=8386"}],"version-history":[{"count":9,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/8386\/revisions"}],"predecessor-version":[{"id":8410,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/8386\/revisions\/8410"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=8386"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=8386"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=8386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}