{"id":7759,"date":"2021-11-06T01:16:22","date_gmt":"2021-11-05T19:46:22","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7759"},"modified":"2021-11-06T01:36:03","modified_gmt":"2021-11-05T20:06:03","slug":"what-is-the-integration-of-sin-inverse-root-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/","title":{"rendered":"What is the integration of sin inverse root x ?"},"content":{"rendered":"

Solution :<\/h2>\n

We have, I = \\(sin^{-1}\\sqrt{x}\\) . 1 dx<\/p>\n

By Applying integration by parts,<\/p>\n

Taking \\(sin^{-1}\\sqrt{x}\\) as first function and 1 as second function. Then<\/p>\n

I = \\(sin^{-1}\\sqrt{x}\\) \\(\\int\\) 1 dx – \\(\\int\\) {\\(d\\over dx\\)\\(sin^{-1}\\sqrt{x}\\) \\(\\int\\) 1 dx } dx<\/p>\n

I = x\\(sin^{-1}\\sqrt{x}\\) – \\(\\int\\) \\(1\\over 2\\sqrt{(1-x)}\\sqrt{x}\\) . x dx<\/p>\n

I = x\\(sin^{-1}\\sqrt{x}\\) – \\(\\int\\) \\(1\\over 2\\) \\(\\sqrt{x}\\over \\sqrt{(1-x)}\\) dx<\/p>\n

Put x = \\(sin^2 t\\)<\/p>\n

dx = 2 sin t cos t dt<\/p>\n

\\(\\implies\\) I = x\\(sin^{-1}\\sqrt{x}\\) – { \\(1\\over 2\\) \\(\\int\\) \\(2sin^2 t\\) dt }<\/p>\n

\\(\\implies\\) I = x\\(sin^{-1}\\sqrt{x}\\)\u00a0 – { \\(1\\over 2\\) \\(\\int\\) (1 – cos 2t) dt }<\/p>\n

\\(\\implies\\) I = x\\(sin^{-1}\\sqrt{x}\\) – \\(1\\over 2\\)t + \\(1\\over 4\\)\\(sin 2t\\) + C<\/p>\n

Now, sin 2t = 2 sin t cos t = \\(2\\sqrt{x} \\sqrt{1 – x}\\) = \\(2\\sqrt{x – x^2}\\)<\/p>\n

I = x\\(sin^{-1}\\sqrt{x}\\) – \\(1\\over 2\\)\\(sin^{-1}\\sqrt{x}\\) + \\(1\\over 4\\) (\\(2\\sqrt{x – x^2}\\))\u00a0 + C<\/p>\n

I = (x – \\({1\\over 2}\\))\\(sin^{-1}\\sqrt{x}\\) + \\(1\\over 2\\) \\(\\sqrt{x – x^2}\\) \u00a0+ C<\/p>\n

\n

Similar Questions<\/h3>\n

What is integration of sin inverse cos x ?<\/a><\/p>\n

What is the integration of sin inverse x whole square ?<\/a><\/p>\n

What is the integration of x sin inverse x dx ?<\/a><\/p>\n

What is the integration of tan inverse root x ?<\/a><\/p>\n

What is the integration of x tan inverse x dx ?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have, I = \\(sin^{-1}\\sqrt{x}\\) . 1 dx By Applying integration by parts, Taking \\(sin^{-1}\\sqrt{x}\\) as first function and 1 as second function. Then I = \\(sin^{-1}\\sqrt{x}\\) \\(\\int\\) 1 dx – \\(\\int\\) {\\(d\\over dx\\)\\(sin^{-1}\\sqrt{x}\\) \\(\\int\\) 1 dx } dx I = x\\(sin^{-1}\\sqrt{x}\\) – \\(\\int\\) \\(1\\over 2\\sqrt{(1-x)}\\sqrt{x}\\) . x dx I = x\\(sin^{-1}\\sqrt{x}\\) – …<\/p>\n

What is the integration of sin inverse root x ?<\/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":[52,43],"tags":[],"yoast_head":"\nWhat is the integration of sin inverse root x ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the integration of sin inverse root x by using integration by parts.\" \/>\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-the-integration-of-sin-inverse-root-x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the integration of sin inverse root x ? - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn what is the integration of sin inverse root x by using integration by parts.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-11-05T19:46:22+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-05T20:06:03+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-the-integration-of-sin-inverse-root-x\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"What is the integration of sin inverse root x ?\",\"datePublished\":\"2021-11-05T19:46:22+00:00\",\"dateModified\":\"2021-11-05T20:06:03+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/\"},\"wordCount\":233,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Integration Questions\",\"Maths Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/\",\"url\":\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/\",\"name\":\"What is the integration of sin inverse root x ? - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-11-05T19:46:22+00:00\",\"dateModified\":\"2021-11-05T20:06:03+00:00\",\"description\":\"In this post you will learn what is the integration of sin inverse root x by using integration by parts.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"What is the integration of sin inverse root x ?\"}]},{\"@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 the integration of sin inverse root x ? - Mathemerize","description":"In this post you will learn what is the integration of sin inverse root x by using integration by parts.","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-the-integration-of-sin-inverse-root-x\/","og_locale":"en_US","og_type":"article","og_title":"What is the integration of sin inverse root x ? - Mathemerize","og_description":"In this post you will learn what is the integration of sin inverse root x by using integration by parts.","og_url":"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/","og_site_name":"Mathemerize","article_published_time":"2021-11-05T19:46:22+00:00","article_modified_time":"2021-11-05T20:06:03+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-the-integration-of-sin-inverse-root-x\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"What is the integration of sin inverse root x ?","datePublished":"2021-11-05T19:46:22+00:00","dateModified":"2021-11-05T20:06:03+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/"},"wordCount":233,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Integration Questions","Maths Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/","url":"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/","name":"What is the integration of sin inverse root x ? - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-11-05T19:46:22+00:00","dateModified":"2021-11-05T20:06:03+00:00","description":"In this post you will learn what is the integration of sin inverse root x by using integration by parts.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-root-x\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"What is the integration of sin inverse root x ?"}]},{"@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\/7759"}],"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=7759"}],"version-history":[{"count":9,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7759\/revisions"}],"predecessor-version":[{"id":7782,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7759\/revisions\/7782"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=7759"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=7759"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=7759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}