{"id":32067,"date":"2023-11-02T14:41:40","date_gmt":"2023-11-02T09:11:40","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=32067"},"modified":"2023-11-03T10:10:30","modified_gmt":"2023-11-03T04:40:30","slug":"ncert-solutions-for-class-12-maths-chapter-7-ex-7-11","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-11\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 7 Integrals Ex 7.11 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.11<\/h2>\n

\"NCERT<\/p>\n

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

Question 2.
\n\\(\\int _{ 0 }^{ \\frac { \\pi }{ 2 } }{ \\frac { \\sqrt { sinx } }{ \\sqrt { sinx } +\\sqrt { cosx } } dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 3.
\n\\(\\int_{0}^{\\frac{\\pi}{2}} \\frac{\\sin ^{\\frac{3}{2}} x d x}{\\sin ^{\\frac{3}{2}} x+\\cos ^{\\frac{3}{2}} x}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 4.
\n\\(\\int_{0}^{\\frac{\\pi}{2}} \\frac{\\cos ^{5} x d x}{\\sin ^{5} x+\\cos ^{5} x}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 5.
\n\\(\\int_{-5}^{5}|x+2| d x\\)
\nSolution:
\n|x+2| = x + 2 if x + 2 \u2265 0 \u21d2 x \u2265 – 2
\n|x+2| = -(x + 2) if x + 2 < 0 \u21d2 x < – 2
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 6.
\n\\(\\int_{2}^{8}|x-5| d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 7.
\n\\(\\int _{ 0 }^{ 1 }{ x(1-x)^{ n }dx } =I\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 8.
\n\\(\\int _{ 0 }^{ \\frac { \\pi }{ 4 } }{ log(1+tanx)dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 9.
\n\\(\\int_{0}^{2} x \\sqrt{2-x} d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 10.
\n\\(\\int_{0}^{\\frac{\\pi}{2}}(2 \\log \\sin x-\\log \\sin 2 x)\\)dx
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 11.
\n\\(\\int_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}} \\sin ^{2} x d x\\)
\nSolution:
\nHere f(x) = sin\u00b2x
\n\u2234 f(x) = sin\u00b2(-x) = [sin(-x)]\u00b2
\n= (-sinx)\u00b2 = sin\u00b2x
\nSince f(-x) = f(x),
\nf(x) = sin\u00b2x is an even function.
\n\"NCERT<\/p>\n

Question 12.
\n\\(\\int_{0}^{\\pi} \\frac{x d x}{1+\\sin x}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 13.
\n\\(\\int _{ \\frac { -\\pi }{ 2 } }^{ \\frac { \\pi }{ 2 } }{ { sin }^{ 7 } } xdx\\)
\nSolution:
\nLet f(x) = sin7<\/sup> xdx
\n\u21d2 f(-x) = -sin7<\/sup> x = -f(x)
\n\u21d2 f(x) is an odd function of x
\n\u21d2 \\(\\int _{ \\frac { -\\pi }{ 2 } }^{ \\frac { \\pi }{ 2 } }{ { sin }^{ 7 } } xdx=0\\)<\/p>\n

Question 14.
\n\\(\\int _{ 0 }^{ 2\\pi }{ { cos }^{ 5 } } xdx\\)
\nSolution:
\nLet f(x) = cos5<\/sup> x
\nf(2\u03c0 – x) = cos5<\/sup>(2\u03c0 – x) = cos5<\/sup> x
\nf(2\u03c0 – x) = f(x)
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 15.
\n\\(\\int _{ 0 }^{ \\frac { \\pi }{ 2 } }{ \\frac { sinx-cosx }{ 1+sinx\\quad cosx } dx } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 16.
\n\\(\\int_{0}^{\\pi} \\log (1+\\cos x) d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 17.
\n\\(\\int_{0}^{a} \\frac{\\sqrt{x}}{\\sqrt{x}+\\sqrt{a-x}} d x\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 18.
\n\\(\\int_{0}^{4}|x-1| d x\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 19.
\nShow that \\(\\int_{0}^{a} f(x) g(x) d x=2 \\int_{0}^{a} f(x) d x\\) if f and g are defined as f(x) = f(a – x) and g(x) + g(a – x) = 4
\nSolution:
\n\"NCERT<\/p>\n

Question 20.
\nThe value of
\n\\(\\int _{ \\frac { -\\pi }{ 2 } }^{ \\frac { \\pi }{ 2 } }{ \\left( { x }^{ 3 }+xcosx+{ tan }^{ 5 }x+1 \\right) dx } \\) is
\n(a) 0
\n(b) 2
\n(c) \u03c0
\n(d) 1
\nSolution:
\n(c) \u03c0
\nLet f(x) = x\u00b3 + x cosx + tan5<\/sup>x
\nf(- x) = (- x)\u00b3 + (- x)cos(- x) + tan5(- x)
\n= – x\u00b3 – x cosx – tan5x
\n= – f(x)
\n\u2234 f(x) is an odd function
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 21.
\nThe value of \\(\\int_{0}^{\\frac{x}{2}} \\log \\left(\\frac{4+3 \\sin x}{4+3 \\cos x}\\right) d x\\) is
\n(a) 2
\n(b) \\(\\frac { 3 }{ 4 }\\)
\n(c) 0
\n(d) – 2
\nSolution:
\n\"NCERT
\nI = – 1
\n2I = 0 Hence I = 0
\nEvaluate the following.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.11 Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: |x+2| = x + 2 if …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11<\/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":{"spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11 - NCERT Solutions<\/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:\/\/ncertsolutions.guru\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-11\/\" \/>\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 7.11 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11 Questions and Answers are prepared by our highly skilled subject experts. 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