{"id":31964,"date":"2022-03-29T14:30:10","date_gmt":"2022-03-29T09:00:10","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=31964"},"modified":"2022-03-29T15:43:09","modified_gmt":"2022-03-29T10:13:09","slug":"ncert-solutions-for-class-12-maths-chapter-7-ex-7-6","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-6\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.6"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 7 Integrals Ex 7.6 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-6\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.6<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\nx sinx
\nSolution:
\nBy part integration
\n\u222bx sinx dx = x(-cosx) – \u222b1(-cosx)dx
\n= – x cosx + \u222bcosxdx
\n= – x cosx + sinx + c<\/p>\n

Question 2.
\nx sin 3x
\nSolution:
\n\u222bxsin 3x dx = x \u222bsin 3 dx – \u222b(\\(\\frac { d }{ dx }\\)(x) \u222bsin 3x dx)dx
\n= \\(=x\\left(\\frac{-\\cos 3 x}{3}\\right)-\\int 1\\left(\\frac{-\\cos 3 x}{3}\\right) d x\\)
\n= \\(\\frac{-1}{3} x \\cos 3 x+\\frac{1}{9} \\sin 3 x+C\\)<\/p>\n

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

Question 4.
\nx logx
\nSolution:
\n\"NCERT<\/p>\n

Question 5.
\nx log 2x
\nSolution:
\n\"NCERT<\/p>\n

Question 6.
\n\\({ x }^{ 2 }logx\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 7.
\nx sin-1<\/sup> x
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 8.
\nx tan-1<\/sup> x
\nSolution:
\n\\(I=x\\quad { tan}^{ -1 }x.\\left( \\frac { { x }^{ 2 } }{ 2 } \\right) -\\int { \\frac { 1 }{ \\sqrt { 1+{ x }^{ 2 } } } } .\\frac { { x }^{ 2 } }{ 2 } dx\\)
\n\\(=\\frac { { x }^{ 2 } }{ 2 } { tan }^{ -1 }x-\\frac { 1 }{ 2 } \\int { \\left( 1-\\frac { 1 }{ 1+{ x }^{ 2 } } \\right) dx } \\)
\n\\(=\\frac { { x }^{ 2 } }{ 2 } { tan }^{ -1 }x-\\frac { 1 }{ 2 } x+\\frac { 1 }{ 2 } { tan }^{ -1 }\\)<\/p>\n

Question 9.
\nx cos-1<\/sup> x
\nSolution:
\n\"NCERT<\/p>\n

Question 10.
\n(sin-1<\/sup> x)\u00b2
\nSolution:
\nMethod I
\nTake 1 as the second function and integrate, w.r.t. x
\n\"NCERT<\/p>\n

Method II
\n\"NCERT<\/p>\n

Method III
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 11.
\n\\(\\frac{x \\cos ^{-1} x}{\\sqrt{1-x^{2}}}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 12.
\nx sec\u00b2x
\nSolution:
\n\u222bx sec\u00b2x dx
\n= \\(x \\int \\sec ^{2} x d x-\\int\\left(\\frac{d}{d x}(x) \\int \\sec ^{2} x d x\\right) d x\\)
\n= x tan x -\u222btan x dx
\n= x tan x – log |sec x| + C
\n= x tan x + log |cos x| + C<\/p>\n

Question 13.
\ntan-1<\/sup> x
\nSolution:
\n\\(\\int { { tan }^{ -1 }xdx } =x{ tan }^{ -1 }x-\\frac { 1 }{ 2 } \\int { \\frac { 2x }{ 1+{ x }^{ 2 } } dx } \\)
\n\\(=x{ tan }^{ -1 }x-\\frac { 1 }{ 2 } log|1+{ x }^{ 2 }|+C \\)<\/p>\n

Question 14.
\nx(logx)\u00b2
\nSolution:
\n\"NCERT<\/p>\n

Question 15.
\n(x\u00b2 + 1) log x
\nSolution:
\n\"NCERT<\/p>\n

Question 16.
\n\\({ e }^{ x }(sinx+cosx)\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 17.
\n\\(\\frac { { xe }^{ x } }{ { (1+x) }^{ 2 } } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 18.
\n\\(\\frac { { e }^{ x }(1+sinx) }{ 1+cosx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 19.
\n\\({ e }^{ x }\\left( \\frac { 1 }{ x } -\\frac { 1 }{ { x }^{ 2 } } \\right) \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 20.
\n\\(\\frac { { (x-2)e }^{ x } }{ { (x-1) }^{ 3 } } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 21.
\n\\({ e }^{ 2x }sinx\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 22.
\n\\(\\sin ^{-1}\\left(\\frac{2 x}{1+x^{2}}\\right)\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 23.
\n\\(\\int { { x }^{ 2 }{ e }^{ { x }^{ 3 } } } dx\\quad equals\\)
\n(a) \\(\\frac { 1 }{ 3 } { e }^{ { x }^{ 3 } }+C\\)
\n(b) \\(\\frac { 1 }{ 3 } +{ e }^{ { x }^{ 2 } }+C\\)
\n(c) \\(\\frac { 1 }{ 2 } { e }^{ { x }^{ 3 } }+C\\)
\n(d) \\(\\frac { 1 }{ 2 } { e }^{ { x }^{ 2 } }+C\\)
\nSolution:
\n(a) \\(\\frac { 1 }{ 3 } { e }^{ { x }^{ 3 } }+C\\)
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 24.
\n\\(\\int { { e }^{ x }secx(1+tanx) } dx\\quad equals\\)
\n(a) \\({ e }^{ x }cosx+C\\)
\n(b) \\({ e }^{ x }secx+C\\)
\n(c) \\({ e }^{ x }sinx+C\\)
\n(d) \\({ e }^{ x }tanx+C\\)
\nSolution:
\n(b) \\({ e }^{ x }secx+c\\)
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.6 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-6\/ NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.6 Question 1. x sinx Solution: By part integration \u222bx sinx dx = x(-cosx) – \u222b1(-cosx)dx = – x cosx + …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.6<\/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 7.6 - 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-7-6\/\" \/>\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 7.6 - 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