{"id":32025,"date":"2022-03-29T15:30:03","date_gmt":"2022-03-29T10:00:03","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=32025"},"modified":"2022-03-29T15:46:52","modified_gmt":"2022-03-29T10:16:52","slug":"ncert-solutions-for-class-12-maths-chapter-7-ex-7-9","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-9\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 7 Integrals Ex 7.9 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-9\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.9<\/h2>\n

\"NCERT<\/p>\n

Ncert Solutions Of Class 12 Maths Chapter 7 Question 1.<\/strong>
\n\\(\\int_{-1}^{1}(x+1)\\)
\nSolution:
\nLet I = \\(\\int_{-1}^{1}(x+1)\\) dx
\n= \\(\\left[\\frac{x^{2}}{2}+x\\right]_{-1}^{1}\\)
\n= \\(\\left(\\frac{1}{2}+1\\right)-\\left(\\frac{1}{2}-1\\right)=\\frac{3}{2}+\\frac{1}{2}=2\\)<\/p>\n

Ex 7.9 Class 12 NCERT Solutions Question 2.<\/strong>
\n\\(\\int _{ 2 }^{ 3 }{ \\frac { 1 }{ x } dx } \\)
\nSolution:
\nLet I = \\(\\int_{2}^{3} \\frac{1}{x} d x=[\\log |x|]_{2}^{3}\\)
\n= \\(\\log 3-\\log 2=\\log \\frac{3}{2}\\)<\/p>\n

Question 3.
\n\\(\\int _{ 1 }^{ 2 }{ \\left( { 4x }^{ 3 }-{ 5x }^{ 2 }+6x+9 \\right) dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 4.
\n\\(\\int_{0}^{\\frac{\\pi}{4}} \\sin 2 x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 5.
\n\\(\\int_{0}^{\\frac{\\pi}{2}} \\cos 2 x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 6.
\n\\(\\int _{ 4 }^{ 5 }{ { e }^{ x }dx } \\)
\nSolution:
\nLet I = \\(\\int _{ 4 }^{ 5 }{ { e }^{ x }dx } \\)
\n= \\(\\left[e^{x}\\right]_{4}^{5}=e^{5}-e^{4}\\)
\n= e4<\/sup> (e – 1)<\/p>\n

\"NCERT<\/p>\n

Question 7.
\n\\(\\int_{0}^{\\frac{\\pi}{4}} \\tan x \\)
\nSolution:
\n\\(\\int_{0}^{\\frac{\\pi}{4}} \\tan x d x\\)
\n= \\(\\left[\\log |\\sec x|_{0}^{\\frac{x}{4}}\\right.\\)
\n= \\(\\log \\left|\\sec \\frac{\\pi}{4}\\right|-\\log |\\sec 0|=\\log \\sqrt{2}-\\log 1=\\log \\sqrt{2}\\)<\/p>\n

Question 8.
\n\\(\\int_{\\frac{\u03c0}{6}}^{\\frac{\u03c0}{4}}\\) cosec x dx
\nSolution:
\n\"NCERT<\/p>\n

Question 9.
\n\\(\\int _{ 0 }^{ 1 }{ \\frac { dx }{ \\sqrt { 1-{ x }^{ 2 } } } } \\)
\nSolution:
\nLet I = \\(\\int_{0}^{1} \\frac{d x}{\\sqrt{1-x^{2}}}=\\left[\\sin ^{-1} x\\right]_{0}^{1}\\)
\n= \\(\\sin ^{-1}(1)-\\sin ^{-1}(0)=\\frac{\\pi}{2}-0=\\frac{\\pi}{2}\\)<\/p>\n

Question 10.
\n\\(\\int _{ 0 }^{ 1 }{ \\frac { dx }{ 1+{ x }^{ 2 } } } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 11.
\n\\(\\int _{ 2 }^{ 3 }{ \\frac { dx }{ { x }^{ 2 }-1 } } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 12.
\n\\(\\int _{ 0 }^{ \\frac { \\pi }{ 2 } }{ { cos }^{ 2 } } x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 13.
\n\\(\\int _{ 2 }^{ 3 }{ \\frac { x }{ { x }^{ 2 }+1 } }\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 14.
\n\\(\\int _{ 0 }^{ 1 }{ \\frac { 2x+3 }{ { 5x }^{ 2 }+1 } } \\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 15.
\n\\(\\int _{ 0 }^{ 1 }{ { xe }^{ { x }^{ 2 } }dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 16.
\n\\(\\int _{ 1 }^{ 2 }{ \\frac { { 5x }^{ 2 } }{ { x }^{ 2 }+4x+3 } dx } \\)
\nSolution:
\n\"NCERT
\n20x + 15A(x + 3) + B(x + 1) …. (2)
\nPut x = – 1 in (2), we get
\n– 5 = 2A \u2234 A = \\(\\frac { – 5 }{ 2 }\\)
\nPut x = – 3 in (2), we get
\n– 45 = – 2B \u2234 B = \\(\\frac { 45 }{ 2 }\\)
\n\"NCERT<\/p>\n

Question 17.
\n\\(\\int _{ 0 }^{ \\frac { \\pi }{ 4 } }{ \\left( { 2sec }^{ 2 }x+{ x }^{ 3 }+2 \\right) dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 18.
\n\\(\\int _{ 0 }^{ \\pi }{ \\left( { sin }^{ 2 }\\frac { x }{ 2 } -{ cos }^{ 2 }\\frac { x }{ 2 } \\right) }\\)dx
\nSolution:
\n\"NCERT<\/p>\n

Question 19.
\n\\(\\int _{ 0 }^{ 2 }{ \\frac { 6x+3 }{ { x }^{ 2 }+4 } } dx\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 20.
\n\\(\\int _{ 0 }^{ 1 }{ \\left( { xe }^{ x }+sin\\frac { \\pi x }{ 4 } \\right) dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 21.
\n\\(\\int_{1}^{\\sqrt{3}} \\frac{d x}{1+x^{2}}\\) equals
\n(a) \\(\\frac { \\pi }{ 3 } \\)
\n(b) \\(\\frac { 2\\pi }{ 3 } \\)
\n(c) \\(\\frac { \\pi }{ 6 } \\)
\n(d) \\(\\frac { \\pi }{ 12 } \\)
\nSolution:
\n(d) \\(\\frac { \\pi }{ 12 } \\)
\nLet I = \\(\\int_{1}^{\\sqrt{3}} \\frac{d x}{1+x^{2}}\\)
\n= \\(\\left[\\tan ^{-1} x\\right]_{1}^{\\sqrt{3}}=\\tan ^{-1} \\sqrt{3}-\\tan ^{-1} 1\\)
\n= \\(\\frac{\\pi}{3}-\\frac{\\pi}{4}=\\frac{\\pi}{12}\\)<\/p>\n

\"NCERT<\/p>\n

Question 22.
\n\\(\\int_{0}^{\\frac{2}{3}} \\frac{d x}{4+9 x^{2}}\\) equals
\n(a) \\(\\frac { \\pi }{ 6 }\\)
\n(b) \\(\\frac { \\pi }{ 12 }\\)
\n(c) \\(\\frac { \\pi }{ 24 }\\)
\n(d) \\(\\frac { \\pi }{ 4 }\\)
\nSolution:
\n(c) \\(\\frac { \\pi }{ 24 }\\)
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-9\/ NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.9 Ncert Solutions Of Class 12 Maths Chapter 7 Question 1. Solution: Let I = dx = = Ex 7.9 Class …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9<\/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 7.9 - 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-7-9\/\" \/>\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 7.9 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-9\/ NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.9 Ncert Solutions Of Class 12 Maths Chapter 7 Question 1. 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