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>\nNCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.7<\/h2>\n <\/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 <\/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
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Question 5. \n\\(\\sqrt { 1-4x-{ x }^{ 2 } }\\) \nSolution: \n <\/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 <\/p>\n
Question 8. \n\\(\\sqrt { { x }^{ 2 }+3x } \\) \nSolution: \n <\/p>\n
Question 9. \n\\(\\sqrt { 1+\\frac { { x }^{ 2 } }{ 9 } } \\) \nSolution: \n <\/p>\n
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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 \nSolution: \n <\/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 <\/p>\n
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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 <\/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 <\/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 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n