a. 8.2 Suppose that S* f(x) dx = 6, 5+ g(x) dx = 4, and Sf(x) dx = 2. Evaluate the following integrals: - Sa 2f(x) dx (2 Marks) S*(3f(x) - 29(x)) dx (2 Marks) S* f(x)g(x) dx (2 Marks) SIC) dx (2 Marks) C. d. g(x) Sub Total 20 Marksl
4. Given the integrals, [° 8(x) dx =-7, 5*8(x)dx = 6 and 5*g(x) dx = 10, use the properties of integrals to determine the value of the integrals below. a) [°(f(x)+g(x)\dx b) ſ 8(x)dx (4 pts cach) c) $39(x)dx a [ f(x)dx
Question 1 1 pts If f(x)dx = 10 and Să f(x) = 3.6, find si f(x)dx. 6.4 Question 2 1 pts Let Só f(x)dx = 6, Sº f(x)dx = -4, So g(x)dx = 12, S g(x)dx = 9 Use these values to evaluate the given definite integral: Si (35(x) + 2g(x))dx —
9. Suppose that we are given the following information about the functions f,g and their deriva- tives and integrals; =4 f(0) = 0 • f(1) = • f'(1) = 2 g(0) = 5 g(1) = 4 • g'(1) =-2 So f(x)dx = 8 5* |(x)dx = 5 Sa f(x)dx = 11 S3 f (x)dx = 6 (d) (5 points) Evaluate Si f(x)dx. (e) (6 points) Evaluate ( f (.5.1 + 4)d.. (f) (6 points) Evaluate, (ثم) (g) (6 points) Evaluate,...
(1 point) Using Properties of Definite Integrals. Given S f(x) fo dx = 0 and f(x) dx = 6 evaluate (a) f(x) dx = (b) f(x) dx - Liro f(x) dx = (c) L.ro 3f(x) dx = (d) $350 38(x) dx Note: You can earn partial credit on this problem. Preview Mv Answers Submit Answers 19
6.a) Let -2 5 -6 10 ), 2) an Evaluate the matrix 8 marks) b) Find the area enclosed between the following curves and sketch the region. 5x2-2. f(x)--3x2 + 30 and g(x) marks) c) Evaluate the following integrals. Give your answers to 2 decimal places. dac i) 2 (3+2 dx. (8 marks) [25 marks] 6.a) Let -2 5 -6 10 ), 2) an Evaluate the matrix 8 marks) b) Find the area enclosed between the following curves and sketch...
(3 points) Let $*fdx = 5, $*f6wdx=-11, 6 s6wdx= 11, $* sco) dx = 4, Use these values to evaluate the given definite integrals. 2 a) / (f(x) + g(x)) dx = b) fºr(x) = g(x) dx = on f* 3F() +29(e) dx = d) Find the value a such that / (af(x) + g(x)) dx = 0. a =
(2) Find the values of land g with l> 0 and g > 0 that maximize the utility function U = f(l,g) = 844/591/5 subject to the constraint 10l + 8g = 40. (2) Suppose So f(x) dx = 7, Sº f(x) dx = -3, and Søg(x) dx = 2. Evaluate the following integrals: (a) 195f (x) dx (b) Sš (–39(2)) da (c) S (3f(x) — 9(z)) da (d) S8 (f(x) + 2g(x)) dx
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
If Si f(x)da = 12 and so f(x) = 2.8, find si f(x)dx. Question 2 1 pts Let f(x)dx = 6, S. 8(x)dx = -4, S g(x)da = 12, g(x)dx = 9 Use these values to evaluate the given definite integral: (+1) da