{"id":31946,"date":"2023-11-02T17:54:59","date_gmt":"2023-11-02T12:24:59","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=31946"},"modified":"2023-11-03T10:08:26","modified_gmt":"2023-11-03T04:38:26","slug":"ncert-solutions-for-class-12-maths-chapter-7-ex-7-8","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-8\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.8"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 7 Integrals Ex 7.8 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.8<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\n\\(\\int_{a}^{b} x d x\\)
\nSolution:
\nLet I = \\(\\int_{a}^{b} x d x\\)
\nf(x) = x, nh = b – a
\nf(a) = a
\nf[a + h) = a + h
\nf(a + 2 h) = a+ 2h,
\n……………………….
\nf[a + (n – 1)h) = a + (n – 1)h
\n\"NCERT<\/p>\n

Question 2.
\n\\(\\int_{0}^{5}(x+1) d x\\)
\nSolution:
\nLet I = \\(\\int_{0}^{5}(x+1) d x\\)
\nWe have a = 0, b = 5 and f(x) = x + 1
\nnh = b-a = 5 – 0 = 5
\nf(0) = 0 + 1 = 1
\nf(0 + h) = 0 + h + 1 = h + 1
\nf(0 + 2h) = 0 + 2h + 1 = 2h + 1
\n………………………….
\nf(0 + (n – 1 )h) = 0 + (n – 1)h + 1 = (n – 1)h + 1
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 3.
\n\\(\\int_{2}^{3} x^{2} d x\\)
\nSolution:
\nLet I = \\(\\int_{2}^{3} x^{2} d x\\)
\nf(x) = x\u00b2, a = 2, b = 3, nh = b – a = 3 – 2 = 1
\nf(2) = 2\u00b2 = 4,
\nf(2 + h) = (2 + h)\u00b2 = 4 + h\u00b2 + 4h
\nf(2 + 2h) = (2 + 2h)\u00b2 = 4+ 4h\u00b2 + 8h
\n………………………….
\nf(2 + (n – 1 )h) = (2 + (n – 1)h]\u00b2 = 4 + (h – 1)\u00b2h\u00b2 + 4(n – 1)h
\n\"NCERT<\/p>\n

Question 4.
\n\\(\\int_{1}^{4}\\left(x^{2}-x\\right) d x\\)
\nSolution:
\nLet I = \\(\\int_{1}^{4}\\left(x^{2}-x\\right) d x\\)
\nWe have a = 1, b = 4, f(x) = x\u00b2 – x and nh = b – a = 4 – 1 = 3
\nf(1) = 1\u00b2 – 1 = 0
\nf(1 + h) = (1 + h)\u00b2 – (1 + h) = h\u00b2 + h
\nf(1 + 2h) = (1 + 2h)\u00b2 – (1 + 2 h) = 2\u00b2h\u00b2 + 2 h
\n………………………….
\nf(1 + n – 1)h) = [1 + (n – 1)h]\u00b2 – [1 + (n – 1)h] = (n – 1)\u00b2 h\u00b2 +(n – 1 )h
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 5.
\n\\(\\int_{-1}^{1} e^{x} d x\\)
\nSolution:
\nLet I = \\(\\int_{-1}^{1} e^{x} d x\\)
\nWe have a = – 1, b = 1, f(x) = ex<\/sup>, nh = b – a = 1 + 1 = 2
\nf(- 1) = e-1<\/sup>
\nf(- 1 + h) = e-1+h<\/sup>
\nf(- 1 + 2h) = e-1+2h<\/sup>
\n………………………….
\nf(- 1 + (n – h)h) = e-1+(n-1)h<\/sup>
\n\"NCERT<\/p>\n

Question 6.
\n\\(\\int_{0}^{4}\\left(x+e^{2 x}\\right) d x\\)
\nSolution:
\nLet I = \\(\\int_{0}^{4}\\left(x+e^{2 x}\\right) d x\\)
\nf(x) = x + e2x<\/sup>
\na = 0, b = 4, nh = b – a = 4 – 0 = 4
\nf(0) = 0 + e0<\/sup> = 1
\nf(0 + h) = (0 + h) + e2(0+h)<\/sup> = h + e2h<\/sup>
\nf(0 + 2h) = (0 + 2h) + e2(0+h)<\/sup> = 2h + e2h<\/sup>
\n………………………….
\nf(0 + (n – 1)h) = (0 + (n – 1 )h) + e2(0+h)<\/sup>=(n – 1 )h + e2(n-1)h<\/sup>
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.8 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.8 Question 1. Solution: Let I = f(x) = x, nh = b – a f(a) = a f[a + h) = …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.8<\/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 7.8 - 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-7-8\/\" \/>\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 7.8 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.8 Questions and Answers are prepared by our highly skilled subject experts. 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