{"id":8383,"date":"2021-11-21T00:38:51","date_gmt":"2021-11-20T19:08:51","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8383"},"modified":"2021-11-21T01:14:18","modified_gmt":"2021-11-20T19:44:18","slug":"what-is-newton-leibnitz-formula-with-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/","title":{"rendered":"What is Newton Leibnitz formula with Examples ?"},"content":{"rendered":"

Newton Leibnitz formula<\/h2>\n

If h(x) and g(x) are differentiable functions of x then,<\/p>\n

\n

\\(d\\over dx\\) \\(\\int_{g(x)}^{h(x)}\\) f(t)dt = f[h(x)].h'(x) – f[g(x)].g'(x)<\/p>\n<\/blockquote>\n

Example<\/strong><\/span> : Evaluate \\(d\\over dt\\) \\(\\int_{t^2}^{t^3}\\) \\(1\\over log x\\) dx<\/p>\n

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

\\(d\\over dt\\) \\(\\int_{t^2}^{t^3}\\) \\(1\\over log x\\) dx = \\(1\\over log t^3\\) \\(d\\over dt\\) \\((t^3)\\) – \\(1\\over log t^2\\) \\(d\\over dt\\) \\((t^2)\\)<\/p>\n

= \\(3t^2\\over 3 log t\\) – \\(2t\\over 2 log t\\) = \\(t(t – 1)\\over log t\\)<\/p>\n\n\n

\n
Next – Walli’s Formula in Integration<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Properties and Formulas for Definite Integrals<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Newton Leibnitz formula If h(x) and g(x) are differentiable functions of x then, \\(d\\over dx\\) \\(\\int_{g(x)}^{h(x)}\\) f(t)dt = f[h(x)].h'(x) – f[g(x)].g'(x) Example : Evaluate \\(d\\over dt\\) \\(\\int_{t^2}^{t^3}\\) \\(1\\over log x\\) dx Solution : We have, \\(d\\over dt\\) \\(\\int_{t^2}^{t^3}\\) \\(1\\over log x\\) dx = \\(1\\over log t^3\\) \\(d\\over dt\\) \\((t^3)\\) – \\(1\\over log t^2\\) \\(d\\over dt\\) …<\/p>\n

What is Newton Leibnitz formula with Examples ?<\/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":[204,207,208],"yoast_head":"\nWhat is Newton Leibnitz formula with Examples ?<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is newton leibnitz formula 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-newton-leibnitz-formula-with-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is Newton Leibnitz formula with Examples ?\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn what is newton leibnitz formula in definite integration with examples.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-11-20T19:08:51+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-20T19:44:18+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-newton-leibnitz-formula-with-examples\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"What is Newton Leibnitz formula with Examples ?\",\"datePublished\":\"2021-11-20T19:08:51+00:00\",\"dateModified\":\"2021-11-20T19:44:18+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/\"},\"wordCount\":113,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"integration\",\"newton leibnitz formula\",\"newton leibniz formula jee\"],\"articleSection\":[\"Definite Integration\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/\",\"url\":\"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/\",\"name\":\"What is Newton Leibnitz formula with Examples ?\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-11-20T19:08:51+00:00\",\"dateModified\":\"2021-11-20T19:44:18+00:00\",\"description\":\"In this post you will learn what is newton leibnitz formula in definite integration with examples.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"What is Newton Leibnitz formula with Examples ?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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