{"id":7788,"date":"2021-11-06T14:08:46","date_gmt":"2021-11-06T08:38:46","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7788"},"modified":"2021-11-06T15:36:48","modified_gmt":"2021-11-06T10:06:48","slug":"what-is-the-integration-of-sec-inverse-root-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-sec-inverse-root-x\/","title":{"rendered":"What is the integration of sec inverse root x ?"},"content":{"rendered":"

Solution :<\/h2>\n

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

Let x = \\(sec^2t\\)<\/p>\n

dx = \\(2sec^2 t tan t\\) dt<\/p>\n

I = t.\\(2sec^2 t tan t\\) dt<\/p>\n

u = t\u00a0 and v = \\(tan^2 t\\)<\/p>\n

I = \\(\\int\\) u.dv = u.v – \\(\\int\\) v.du = \\(t.tan^2 t\\) – \\(\\int\\) \\(tan^2 t\\) dt<\/p>\n

I = \\(t.tan^2 t\\) – \\(\\int\\) \\(sec^2 t – 1\\) dt<\/p>\n

I = \\(t.tan^2 t\\) – \\(\\int\\) \\(sec^2 t\\) + \\(int\\) 1 dt<\/p>\n

I = \\(t.tan^2 t\\) – tan t + t + C = \\(t.sec^2 t\\) – tan t + C<\/p>\n

I = \\(xsec^{-1}\\sqrt{x}\\) – \\(\\sqrt{sec^2t – 1}\\) + C<\/p>\n

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

\n

Similar Questions<\/h3>\n

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

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

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

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

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

Solution : We have, I = \\(sec^{-1}\\sqrt{x}\\) dx Let x = \\(sec^2t\\) dx = \\(2sec^2 t tan t\\) dt I = t.\\(2sec^2 t tan t\\) dt u = t\u00a0 and v = \\(tan^2 t\\) I = \\(\\int\\) u.dv = u.v – \\(\\int\\) v.du = \\(t.tan^2 t\\) – \\(\\int\\) \\(tan^2 t\\) dt I = \\(t.tan^2 t\\) …<\/p>\n

What is the integration of sec 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 sec inverse root x ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the integration of sec 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-sec-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 sec inverse root x ? 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