{"id":154588,"date":"2023-08-05T13:00:00","date_gmt":"2023-08-05T07:30:00","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154588"},"modified":"2023-08-05T13:00:04","modified_gmt":"2023-08-05T07:30:04","slug":"consider-the-line-integral","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/consider-the-line-integral\/","title":{"rendered":"Consider the line integral"},"content":{"rendered":"\n

Q. Consider the line integral<\/p>\n\n\n\n

\u222b(\ud835\udc65\ud835\udc51\ud835\udc66 \u2212 \ud835\udc66\ud835\udc51\ud835\udc65)<\/p>\n\n\n\n

\ud835\udc36<\/p>\n\n\n\n

the integral being taken in a counterclockwise direction over the closed curve \ud835\udc36 that forms the boundary of the region \ud835\udc45 shown in the figure below. The region \ud835\udc45 is the area enclosed by the union of a 2 \u00d7 3 rectangle and a semi-circle of radius 1. The line integral evaluates to<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

(A) 6 + \ud835\udf0b\/2<\/p>\n\n\n\n

(B) 8 + \ud835\udf0b<\/p>\n\n\n\n

(C) 12 + \ud835\udf0b<\/p>\n\n\n\n

(D) 16 + 2\ud835\udf0b<\/p>\n\n\n\n

Ans: 12 + \u03c0<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Q. Consider the line integral \u222b(\ud835\udc65\ud835\udc51\ud835\udc66 \u2212 \ud835\udc66\ud835\udc51\ud835\udc65) \ud835\udc36 the integral being taken in a counterclockwise direction over the closed curve \ud835\udc36 that forms the boundary of the region \ud835\udc45 shown in the figure below. The region \ud835\udc45 is the area enclosed by the union of a 2 \u00d7 3 rectangle and a semi-circle of […]<\/p>\n","protected":false},"author":419,"featured_media":154597,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-154588","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154588","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=154588"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154588\/revisions"}],"predecessor-version":[{"id":154598,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154588\/revisions\/154598"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154597"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154588"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154588"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154588"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}