NCERT Solutions for Class 12 Maths<\/a> Chapter 7 Integrals Ex 7.8 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-8\/<\/p>\nNCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.8<\/h2>\n <\/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 <\/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 <\/p>\n
<\/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 <\/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 <\/p>\n
<\/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 <\/p>\nQuestion 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 <\/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. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-7-ex-7-8\/ 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":{"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 7.8 - 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