{"id":20205,"date":"2024-04-15T05:49:47","date_gmt":"2024-04-15T05:49:47","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20205"},"modified":"2024-04-15T05:49:47","modified_gmt":"2024-04-15T05:49:47","slug":"the-area-enclosed-between-the-curves-y2-4x-and-x2-4y-is-a-frac163-b-8-c-frac323-d-16","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-area-enclosed-between-the-curves-y2-4x-and-x2-4y-is-a-frac163-b-8-c-frac323-d-16\/","title":{"rendered":"The area enclosed between the curves y2 = 4x and x2 = 4y is A. \\[\\frac{{16}}{3}\\] B. 8 C. \\[\\frac{{32}}{3}\\] D. 16"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a9b186570309\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    &#8221;[\frac{{16}}{3}\\                <\/div>\r\n            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    &#8221; option2=&#8221;8&#8243; option3=&#8221;\\[\\frac{{32}}{3}\\]&#8221; option4=&#8221;16&#8243; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The area enclosed between the curves $y^2 = 4x$ and $x^2 = 4y$ is $\\frac{32}{3}$ square units.<\/p>\n<p>To find the area, we can use the following steps:<\/p>\n<ol>\n<li>Find the points of intersection of the two curves.<\/li>\n<li>Set up a definite integral that represents the area enclosed by the curves.<\/li>\n<li>Evaluate the definite integral.<\/li>\n<\/ol>\n<p>The points of intersection of the two curves are $(0,0)$ and $(4,4)$.<\/p>\n<p>The definite integral that represents the area enclosed by the curves is:<\/p>\n<p>$$\\int_0^4 \\left( y^2 &#8211; x^2 \\right) \\, dx$$<\/p>\n<p>Evaluating the definite integral, we get:<\/p>\n<p>$$\\left[ \\frac{y^3}{3} &#8211; \\frac{x^3}{3} \\right]_0^4 = \\frac{64}{3} &#8211; \\frac{64}{3} = \\boxed{\\frac{32}{3}}$$<\/p>\n<p>Here <div class=\"youtube-subscribe-container\">\r\n       <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div>  <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> is a graph of the two curves:<\/p>\n<p>[asy]<br \/>\nunitsize(1 cm);<\/p>\n<p>real ticklen=3;<br \/>\nreal tickspace=1;<br \/>\nreal axisarrowsize=0.14inch;<br \/>\nreal tickdown=-0.5;<br \/>\nreal tickdownlength=-0.12inch;<br \/>\nreal wholetickdown=-0.24inch;<br \/>\nreal wholetickdownlength=-0.2inch;<br \/>\nreal tickdownlengthshort=-0.08inch;<br \/>\nreal wholetickdownlengthshort=-0.12inch;<br \/>\nreal t=0;<br \/>\nreal d=1;<br \/>\nreal xleft=-4;<br \/>\nreal xright=4;<br \/>\nreal ybottom=-4;<br \/>\nreal ytop=4;<\/p>\n<p>draw((xleft,0)&#8211;(xright,0));<br \/>\ndraw((0,ybottom)&#8211;(0,ytop));<\/p>\n<p>real i;<\/p>\n<p>for(i=xleft+tickspace; i&lt;xright; i+=tickspace) {<br \/>\n  draw((i,0.1)&#8211;(i,-0.1));<br \/>\n}<\/p>\n<p>for(i=ybottom+tickspace; i&lt;ytop; i+=tickspace) {<br \/>\n  draw((0.1,i)&#8211;(-0.1,i));<br \/>\n}<\/p>\n<p>label(&#8220;$x$&#8221;,(xright+0.2,0),SE);<br \/>\nlabel(&#8220;$y$&#8221;,(0,ytop+0.2),NW);<\/p>\n<p>draw((0,-0.1)&#8211;(0,0.1));<br \/>\ndraw((0.1,-0.1)&#8211;(0.1,0.1));<\/p>\n<p>label(&#8220;$y^2=4x$&#8221;,(4,2),S);<br \/>\nlabel(&#8220;$x^2=4y$&#8221;,(2,4),E);<\/p>\n<p>draw(graph(y^2=4x,-4,4),red);<br \/>\ndraw(graph(x^2=4y,-4,4),blue);<br \/>\n[\/asy]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8221; option2=&#8221;8&#8243; option3=&#8221;\\[\\frac{{32}}{3}\\]&#8221; option4=&#8221;16&#8243; correct=&#8221;option1&#8243;] Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The area enclosed between the curves y2 = 4x and x2 = 4y is A. \\[\\frac{{16}}{3}\\] B. 8 C. \\[\\frac{{32}}{3}\\] D. 16<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-area-enclosed-between-the-curves-y2-4x-and-x2-4y-is-a-frac163-b-8-c-frac323-d-16\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The area enclosed between the curves y2 = 4x and x2 = 4y is A. \\[\\frac{{16}}{3}\\] B. 8 C. \\[\\frac{{32}}{3}\\] D. 16\" \/>\n<meta property=\"og:description\" content=\"Join Our Telegram Channel Subscribe on YouTube &#8221; 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