{"id":31701,"date":"2021-03-29T15:00:41","date_gmt":"2021-03-29T09:30:41","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=31701"},"modified":"2022-03-29T15:36:59","modified_gmt":"2022-03-29T10:06:59","slug":"ncert-solutions-for-class-12-maths-chapter-7-ex-7-1","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-1\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 7 Integrals Ex 7.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-1\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.1<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\nsin 2x
\nSolution:
\n\"NCERT<\/p>\n

Question 2.
\ncos 3x
\nSolution:
\n\"NCERT<\/p>\n

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

Question 4.
\n(ax + c)\u00b2
\nSolution:
\n\"NCERT<\/p>\n

Question 5.
\nsin 2x – 4 e3x<\/sup>
\nSolution:
\n\"NCERT
\n\u2234 An anti derivative of sin2x – 4e3x<\/sup> is – \\(\\frac { 1 }{ 2 }\\) cos 2x – \\(\\frac { 4 }{ 3 }\\)4e3x<\/sup><\/p>\n

Question 6.
\n\\(\\int { \\left( { 4e }^{ 3x }+1 \\right) dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 7.
\n\\(\\int { { x }^{ 2 }\\left( 1-\\frac { 1 }{ { x }^{ 2 } } \\right) dx } \\)
\nSolution:
\n\\(=\\int { { x }^{ 2 }\\left( 1-\\frac { 1 }{ { x }^{ 2 } } \\right) }dx
\n= \u222b(x\u00b2 – 1)dx
\n= \u222bx\u00b2 dx – \u222b1 dx
\n= [latex]\\frac { { x }^{ 3 } }{ 3 }\\) – x + C<\/p>\n

Question 8.
\n\\(\\int { { (ax }^{ 2 }+bx+c)dx } \\)
\nSolution:
\n\\(\\int { { (ax }^{ 2 }+bx+c)dx } \\)
\n= a\u222bx\u00b2 dx + b \u222bx dx + c\u222b1 dx
\n= \\(\\frac { { ax }^{ 3 } }{ 3 } +\\frac { { bx }^{ 2 } }{ 2 }\\) + cx + C<\/p>\n

Question 9.
\n\\(\\int { \\left( { 2x }^{ 2 }+{ e }^{ x } \\right) dx } \\)
\nSolution:
\n\\(\\int { \\left( { 2x }^{ 2 }+{ e }^{ x } \\right) dx } \\)
\n= 2\u222bx\u00b2 dx + \u222bex<\/sup> dx
\n= 2 \\(\\frac { { x }^{ 3 } }{ 3 }\\) + ex<\/sup> + C
\n= \\(\\frac { { 2x }^{ 3 } }{ 3 } +{ e }^{ x }\\) + C<\/p>\n

Question 10.
\n\\(\\int { { \\left[ \\sqrt { x } -\\frac { 1 }{ \\sqrt { x } } \\right] }^{ 2 }dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 11.
\n\\(\\int { \\frac { { x }^{ 3 }+{ 5x }^{ 2 }-4 }{ { x }^{ 2 } } dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 12.
\n\\(\\int { \\frac { { x }^{ 3 }+3x+4 }{ \\sqrt { x } } dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 13.
\n\\(\\int { \\frac { { x }^{ 3 }-{ x }^{ 2 }+x-1 }{ x-1 } dx } \\)
\nSolution:
\n\\(=\\int { \\frac { { x }^{ 2 }(x-1)+(x-1) }{ x-1 } dx } \\)
\n\\(=\\int { \\left( { x }^{ 2 }+1 \\right) dx } =\\frac { { x }^{ 3 } }{ 3 } +x+c \\)<\/p>\n

Question 14.
\n\\(\\int { \\left( 1-x \\right) \\sqrt { x } dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 15.
\n\\(\\int { \\sqrt { x } \\left( { 3x }^{ 2 }+2x+3 \\right) dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 16.
\n\\(\\int { (2x – 3cosx+{ e }^{ x })dx } \\)
\nSolution:
\n\\(\\int { (2x – 3cosx+{ e }^{ x })dx } \\)
\n= 2\u222bx dx – 3\u222bcosx dx + \u222bex<\/sup> dx
\n= 2(\\(\\frac { { x }^{ 2 } }{ 3 }\\)) – 3 sin x + ex<\/sup> + C
\n\\(={ x }^{ 2 }-3sinx+{ e }^{ x }\\) + C<\/p>\n

Question 17.
\n\\(\\int { \\left( { 2x }^{ 2 }-3sinx+5\\sqrt { x } \\right) dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 18.
\n\\(\\int { secx(secx+tanx)dx } \\)
\nSolution:
\n\\(\\int { secx(secx+tanx)dx } \\)
\n= \\(\\int\\left(\\sec ^{2} x+\\sec x \\tan x\\right) d x\\)
\n= \u222bsec\u00b2 x dx + \u222bsec x tan x dx
\n= tan x + sec + C<\/p>\n

Question 19.
\n\\(\\int { \\frac { { sec }^{ 2 }x }{ { cosec }^{ 2 }x } dx } \\)
\nSolution:
\n= \\(\\int { \\frac { 1 }{ { cos }^{ 2 }x } } { sin }^{ 2 }xdx\\)
\n= \\(\\int { tan } ^{ 2 }xdx\\quad\\)
\n= \\(\\int\\left(\\sec ^{2} x-1\\right) d x\\)
\n= tanx – x + c<\/p>\n

Question 20.
\n\\(\\int { \\frac { 2-3sinx }{ { cos }^{ 2 }x } dx } \\)
\nSolution:
\n= \\(\\int { \\left( \\frac { 2 }{ { cos }^{ 2 }x } -3\\frac { sinx }{ { cos }^{ 2 }x } \\right) dx } \\)
\n= \\(\\int { ({ 2sec }^{ 2 }x-3secxtanx)dx }\\)
\n= 2tanx – 3secx + c<\/p>\n

Choose the correct answer in Exercises 21 and 22.<\/p>\n

Question 21.
\nThe anti derivative \\(\\left( \\sqrt { x } +\\frac { 1 }{ \\sqrt { x } } \\right) \\) equals
\n(a) \\(\\frac { 1 }{ 3 } { x }^{ \\frac { 1 }{ 3 } }+{ 2x }^{ \\frac { 1 }{ 2 } }+c\\)
\n(b) \\(\\frac { 2 }{ 3 } { x }^{ \\frac { 2 }{ 3 } }+{ \\frac { 1 }{ 2 } x }^{ 2 }+c\\)
\n(c) \\(\\frac { 2 }{ 3 } { x }^{ \\frac { 3 }{ 2 } }+{ 2x }^{ \\frac { 1 }{ 2 } }+c\\)
\n(d) \\(\\frac { 3 }{ 2 } { x }^{ \\frac { 3 }{ 2 } }+\\frac { 1 }{ 2 } { x }^{ \\frac { 1 }{ 2 } }+c\\)
\nSolution:
\n(c) \\(\\frac { 2 }{ 3 } { x }^{ \\frac { 3 }{ 2 } }+{ 2x }^{ \\frac { 1 }{ 2 } }+c\\)
\n\"NCERT<\/p>\n

Question 22.
\nIf \\(\\frac { d }{ dx } f(x) = { 4x }^{ 3 } -\\frac { 3 }{ { x }^{ 4 } } \\) such that f(2) = 0 then f(x) is
\n(a) \\({ x }^{ 4 }+\\frac { 1 }{ { x }^{ 3 } } -\\frac { 129 }{ 8 } \\)
\n(b) \\({ x }^{ 3 }+\\frac { 1 }{ { x }^{ 4 } } +\\frac { 129 }{ 8 } \\)
\n(c) \\({ x }^{ 4 }+\\frac { 1 }{ { x }^{ 3 } } +\\frac { 129 }{ 8 } \\)
\n(d) \\({ x }^{ 3 }+\\frac { 1 }{ { x }^{ 4 } } -\\frac { 129 }{ 8 } \\)
\nSolution:
\n(a) \\({ x }^{ 4 }+\\frac { 1 }{ { x }^{ 3 } } -\\frac { 129 }{ 8 } \\)
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-1\/ NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.1 Question 1. sin 2x Solution: Question 2. cos 3x Solution: Question 3. Solution: Question 4. (ax + c)\u00b2 Solution: Question …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1<\/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 7.1 - 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-7-1\/\" \/>\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 7.1 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-1\/ NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.1 Question 1. sin 2x Solution: Question 2. cos 3x Solution: Question 3. 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