{"id":32001,"date":"2022-03-29T15:30:10","date_gmt":"2022-03-29T10:00:10","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=32001"},"modified":"2022-03-29T15:44:05","modified_gmt":"2022-03-29T10:14:05","slug":"ncert-solutions-for-class-12-maths-chapter-7-ex-7-7","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 7 Integrals Ex 7.7 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.7<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\n\\(\\sqrt{4-x^{2}}\\)
\nSolution:
\n\\(\\sqrt{4-x^{2}}\\) dx
\n= \\(\\int \\sqrt{2^{2}-x^{2}} d x\\)
\n= \\(\\frac{x}{2} \\sqrt{2^{2}-x^{2}}+\\frac{4}{2} \\sin ^{-1} \\frac{x}{2}+C\\)
\n= \\(\\frac{x}{2} \\sqrt{4-x^{2}}+2 \\sin ^{-1} \\frac{x}{2}+C\\)<\/p>\n

Question 2.
\n\\(\\sqrt { 1-{ 4x }^{ 2 } } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 3.
\n\\(\\sqrt { { x }^{ 2 }+4x+6 } \\)
\nSolution:
\n\\(\\sqrt { { x }^{ 2 }+4x+6 } \\) dx
\n= \\(\\int \\sqrt{x^{2}+4 x+4+6-4} d x=\\int \\sqrt{(x+2)^{2}+(\\sqrt{2})^{2}} d x\\)
\n= \\(\\frac{x+2}{2} \\sqrt{(x+2)^{2}+(\\sqrt{2})^{2}}+\\frac{2}{2} \\log \\left|(x+2)+\\sqrt{(x+2)^{2}+(\\sqrt{2})^{2}}\\right|+\\mathrm{C}\\)
\n= \\(\\frac{(x+2)}{2} \\sqrt{x^{2}+4 x+6}+\\log \\left|(x+2)+\\sqrt{x^{2}+4 x+6}\\right|+C\\)<\/p>\n

Question 4.
\n\\(\\sqrt{x^{2}+4 x+1}\\)
\nSolution:
\n\\(\\sqrt{x^{2}+4 x+1}\\) dx
\n= \\(\\int \\sqrt{x^{2}+4 x+4+1-4} d x=\\int \\sqrt{(x+2)^{2}-(\\sqrt{3})^{2}} d x\\)
\n= \\(\\frac{(x+2)}{2} \\sqrt{(x+2)^{2}-(\\sqrt{3})^{2}}-\\frac{3}{2} \\log \\left|(x+2)+\\sqrt{(x+2)^{2}-(\\sqrt{3})^{2}}\\right|+\\mathrm{C}\\)
\n= \\(\\frac{(x+2)}{2} \\sqrt{x^{2}+4 x+1}-\\frac{3}{2} \\log \\left|(x+2) \\sqrt{x^{2}+4 x+1}\\right|+C\\)<\/p>\n

\"NCERT<\/p>\n

Question 5.
\n\\(\\sqrt { 1-4x-{ x }^{ 2 } }\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 6.
\n\\(\\sqrt { { x }^{ 2 }+4x-5 } \\)
\nSolution:
\n\\(\\sqrt { { x }^{ 2 }+4x-5 } \\)dx
\n\\(\\int { \\sqrt { { x }^{ 2 }+4x-5 } }\\) dx = \\(\\int { \\sqrt { { (x+2) }^{ 2 }-{ (3) }^{ 2 } } }\\)dx
\n= \\(\\frac { x+2 }{ 2 } \\sqrt { { x }^{ 2 }+4x-5 } -\\frac { 9 }{ 2 } log|x+2+\\sqrt { { x }^{ 2 }+4x-5 } |+c\\)<\/p>\n

Question 7.
\n\\(\\sqrt { 1+3x-{ x }^{ 2 } } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 8.
\n\\(\\sqrt { { x }^{ 2 }+3x } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 9.
\n\\(\\sqrt { 1+\\frac { { x }^{ 2 } }{ 9 } } \\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 10.
\n\\(\\int \\sqrt{1+x^{2}}\\) dx is equal to
\n(a) \\(\\frac { x }{ 2 } \\sqrt { 1+{ x }^{ 2 } } +\\frac { 1 }{ 2 } log|x+\\sqrt { 1+{ x }^{ 2 } } |+C\\)
\n(b) \\(\\frac { 2 }{ 3 } { \\left( 1+{ x }^{ 2 } \\right) }^{ \\frac { 3 }{ 2 } }+C\\)
\n(c) \\(\\frac { 2 }{ 3 } x{ \\left( 1+{ x }^{ 2 } \\right) }^{ \\frac { 3 }{ 2 } }+C\\)
\n(d) \\(\\frac { { x }^{ 2 } }{ 2 } \\sqrt { 1+{ x }^{ 2 } } +\\frac { 1 }{ 2 } { x }^{ 2 }log\\left| x+\\sqrt { 1+{ x }^{ 2 } } \\right| +C\\)
\nSolution:
\n(a) \\(\\frac { x }{ 2 } \\sqrt { 1+{ x }^{ 2 } } +\\frac { 1 }{ 2 } log|x+\\sqrt { 1+{ x }^{ 2 } } |+C\\)
\n\\(\\int { \\sqrt { 1+{ x }^{ 2 } } } \\)dx
\n= \\(\\frac { x }{ 2 } \\sqrt { 1+{ x }^{ 2 } } +\\frac { 1 }{ 2 } log|x+\\sqrt { 1+{ x }^{ 2 } } |+C\\)<\/p>\n

Question 11.
\n\\(\\int \\sqrt{x^{2}-8 x+7}\\) dx
\n\"NCERT
\nSolution:
\n\"NCERT<\/p>\n

Question 12.
\nIntegrate \\(x \\sqrt{x+x^{2}}\\) w.r.t. x.
\nSolution:
\nI = \\(x \\sqrt{x+x^{2}}\\) dx
\nLet x = A\\(\\frac { d }{ dx }\\)(x + x\u00b2) + Bx = A(1 + 2x) + B
\nEquating coefficients of x both sides, we get 2A = 1 \u21d2 A = \\(\\frac { 1 }{ 2 }\\)
\nEquating constants on both sides, we get A + B = 0 \u21d2 B = \\(\\frac { – 1 }{ 2 }\\)
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 13.
\nIntegrate \\((x+1) \\sqrt{2 x^{2}+3}\\) w.r.t. x.
\nSolution:
\nI = \\((x+1) \\sqrt{2 x^{2}+3}\\) dx
\nLet x + 1 = A\\(\\frac { d }{ dx }\\)(2x\u00b2 + 3) + Bx = A(4x) + B
\nEquating the coefficients of x both sides, we get 4A = 1 \u21d2 A = \\(\\frac { 1 }{ 4 }\\)
\nEquating constants on both sides, we get B = 1
\nx + 1 = \\(\\frac { 1 }{ 4 }\\)(4x) + 1
\n\"NCERT<\/p>\n

Question 14.
\nIntegrate \\((x+3) \\sqrt{3-4 x-x^{2}}\\) w.r.t. x.
\nSolution:
\nI = \\((x+3) \\sqrt{3-4 x-x^{2}}\\) dx
\nLet x + 3 = A\\(\\frac { d }{ dx }\\)(3 – 4x – x\u00b2) + Bx + 3 = A(- 4 – 2x) + B
\nEquating the coefficients of x both sides, we get -2A = 1 \u21d2 A = \\(\\frac { – 1 }{ 2 }\\)
\nEquating constants on both sides, we get -4A + B = 3 \u21d2 B = 1
\n\u2234 x + 3 = \\(\\frac { – 1 }{ 2 }\\)(- 4 – 2x) + 1
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/ NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.7 Question 1. Solution: dx = = = Question 2. Solution: Question 3. Solution: dx = = = Question 4. Solution: …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","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":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 - MCQ Questions<\/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:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/ NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.7 Question 1. Solution: dx = = = Question 2. Solution: Question 3. Solution: dx = = = Question 4. Solution: … NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ Questions\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-29T10:00:10+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-29T10:14:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:site\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mcq-questions.com\/#website\",\"url\":\"https:\/\/mcq-questions.com\/\",\"name\":\"MCQ Questions\",\"description\":\"MCQ Questions for Class 1 to 12\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mcq-questions.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"contentUrl\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"width\":170,\"height\":17,\"caption\":\"NCERT Solutions\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#webpage\",\"url\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/\",\"name\":\"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 - MCQ Questions\",\"isPartOf\":{\"@id\":\"https:\/\/mcq-questions.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#primaryimage\"},\"datePublished\":\"2022-03-29T10:00:10+00:00\",\"dateModified\":\"2022-03-29T10:14:05+00:00\",\"author\":{\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\"},\"breadcrumb\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mcq-questions.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7\"}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/mcq-questions.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 - MCQ Questions","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 - MCQ Questions","og_description":"These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/ NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.7 Question 1. Solution: dx = = = Question 2. Solution: Question 3. Solution: dx = = = Question 4. Solution: … NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 Read More »","og_url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/","og_site_name":"MCQ Questions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2022-03-29T10:00:10+00:00","article_modified_time":"2022-03-29T10:14:05+00:00","og_image":[{"url":"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"6 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/mcq-questions.com\/#website","url":"https:\/\/mcq-questions.com\/","name":"MCQ Questions","description":"MCQ Questions for Class 1 to 12","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mcq-questions.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","contentUrl":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","width":170,"height":17,"caption":"NCERT Solutions"},{"@type":"WebPage","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#webpage","url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/","name":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 - MCQ Questions","isPartOf":{"@id":"https:\/\/mcq-questions.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#primaryimage"},"datePublished":"2022-03-29T10:00:10+00:00","dateModified":"2022-03-29T10:14:05+00:00","author":{"@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3"},"breadcrumb":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-7\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mcq-questions.com\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7"}]},{"@type":"Person","@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/mcq-questions.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32001"}],"collection":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/comments?post=32001"}],"version-history":[{"count":2,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32001\/revisions"}],"predecessor-version":[{"id":37756,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32001\/revisions\/37756"}],"wp:attachment":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/media?parent=32001"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/categories?post=32001"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/tags?post=32001"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}