{"id":193448,"date":"2025-02-19T12:04:00","date_gmt":"2025-02-19T12:04:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=193448"},"modified":"2025-02-19T12:04:03","modified_gmt":"2025-02-19T12:04:03","slug":"find-the-total-area-of-the-shaded-regions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/19\/find-the-total-area-of-the-shaded-regions\/","title":{"rendered":"Find the total area of the shaded regions"},"content":{"rendered":"\n

Find the total area of the shaded regions. Ay 30 y=x36 – 2 24 18 12- 6 ? > -10 -8 -6 4-2 2 4 6 8 10 6 -12 18 -24- 30- Find the total area of the shaded regions. ?? 14 H-2,12) 12 (2,12) Jy = 3x\u00b2 10 ob 6 4- 2- y = x – x X -4 -2 2 2 Find the total area of the shaded region. ?? 16 14 12- 10- 8 y=8 6- y=x 4 ?? 32 2- 2 6 8 B 10 12 14 16 Find the total area of the shaded regions. y 12x (3,9) 6 x – 4 2 CO -12 -18 -24 (-3, -27) –X? + 6x<\/p>\n\n\n\n

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

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

It looks like you’re asking about finding the total area of several shaded regions in different mathematical contexts. However, the problem you presented is a bit unclear in terms of formatting and clarity. To proceed, I need to interpret the key parts:<\/p>\n\n\n\n

    \n
  1. You seem to be referencing multiple functions (e.g., ( y = x^2 ), ( y = x – x^2 ), and ( y = 3x^2 )).<\/li>\n\n\n\n
  2. The area likely involves finding the regions between curves on a graph, which can be done by calculating definite integrals for each segment of the region.<\/li>\n\n\n\n
  3. There are coordinates (e.g., (3,9), (2,12)), which may represent points where the curves intersect.<\/li>\n<\/ol>\n\n\n\n

    To accurately calculate the areas of these shaded regions, we would:<\/p>\n\n\n\n

      \n
    1. Identify the curves and the intervals<\/strong>: For each region, find the equations of the curves that define the boundaries.<\/li>\n\n\n\n
    2. Set up the integral(s)<\/strong>: To find the area between the curves, set up integrals for the regions where the functions overlap.<\/li>\n\n\n\n
    3. Calculate the definite integrals<\/strong>: Solve the integrals to find the areas under the curves in the specified intervals.<\/li>\n\n\n\n
    4. Sum the areas<\/strong>: If there are multiple regions, sum the areas found for each one.<\/li>\n<\/ol>\n\n\n\n

      Since the details in your problem seem incomplete or unclear (e.g., the exact boundaries and curves for the shaded regions are not fully specified), please provide a bit more clarity. You can describe the functions and their intersections more clearly, or you can upload a more readable version of the image.<\/p>\n\n\n\n

      I can also generate the image if you’d like! Let me know how you’d like to proceed.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Find the total area of the shaded regions. Ay 30 y=x36 – 2 24 18 12- 6 ? > -10 -8 -6 4-2 2 4 6 8 10 6 -12 18 -24- 30- Find the total area of the shaded regions. ?? 14 H-2,12) 12 (2,12) Jy = 3x\u00b2 10 ob 6 4- 2- y […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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-5)","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-5)","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-5)","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":[25],"tags":[],"class_list":["post-193448","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193448","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=193448"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193448\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193448"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193448"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193448"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}