Question

Let f(x) = 4 - 3x, use 5 rectangles to estimateof each type for the function from x = -4 to x = 6. a) L(5) You can upload your work at: Choose File No file chosen b) R(5) You can upload your work at: Choose File No file chosen c) M(5) You can upload your work at: Choose File No file chosen d) T(5) You can upload your work at: Choose File No file chosen e) Find the net area under the graph of f(x). You can upload your work at: Choose File No file chosen

Answer 1

a) L(5) You can upload your work at: Choose File No file chosen f(20) = f(a) = f(-4) = -44 = -44 f (x1) = f(-2) = -8= -8 f (22) = f(0) = 4 = 4 f (23) = f (2) = -8= -8 f (x4) = f(4) = -44 = -44 Finally, just sum up the above values and multiply by Ax = 2: 2(-44 – 8+4-8 – 44) = -200 Answer: -200. b) R(5) You can upload your work at: Choose File No file chosen f(x1) = f(-2) = -8= -8 f (22) = f(0) = 4 = 4 f (x3) = f (2) = -8= -8 f (x4) = f (4) = -44 = -44 f (25) = f(b) = f (6) = -104 = -104 Finally, just sum up the above values and multiply by Az = 2: 2-8 +4-8 – 44 – 104) = -320 Answer: -320. c) M(5) You can upload your work at: Choose File No file chosen *(** **) = 5(1-4) (-2) = f(-3) = –23 = -23 (****) - - (49)+®) – 8(-1) = 1=1 (****) - s(©(%) – f(1) = 1 - 1 (****) – s (2) (M) – 1 (3) = -23 = -23 (****) - -(19) + ®) – 8 (5) = -71 - -31 Finally, just sum up the above values and multiply by Ax = 2: 21-23 +1+1-23 – 71) = -230 Answer: -230. d) 7(5) You can upload your work at: Choose File No file chosen [ f(x)dx = 4,1% (f(xo) + 2f(+1) +2f(x2)+...+2f(In-1) + f(en)), where Ja b-a Ac=- . We have that a = -4, b = 6, n=5. 6-(-4) Therefore, Ax = - 5 Divide the interval (-4, 6) into n = 5 subintervals of length Ax = 2, with the following endpoints: a= -4,-2,0, 2, 4, 6 = b. f(30) = f(a) = f(-4) = -44 = -44 2f (x1) = 2f (-2) = -16 = -16 2f (22) = 2f(0) = 8 = 8 2f (x3) = 2f (2) = -16 = -16 2f (x4) = 2f (4) = -88 = -88 f (x5) = f(b) = f (6) = -104 = -104 4.2 = 1: Finally, just sum up the above values and multiply by = 1(-44 - 16 + 8 - 16 - 88 - 104) = -260 Answer: -260. e) Find the net area under the graph of f(x). You can upload your work at: Choose File No file chosen 964-22) de = 4(60) = 5(6°+49) = 80 – (286+ 64) = -240

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