Question

15.16 points LarsonETS 5.3.048 My Notes Ask Your The graph of f consists of line segments, as shown in the figure. Evaluate each definite integral by using geometric formulas. 3.2) 4,2) 1 1 23456810 -2 -3 8,-2 (a)) dk (b) 2x) dx (c)x) dx (d) f" (d)-7x) dx (e) x) dx 10 Need Help? Taik to Tuter Submit Answer Save Progress

Answer 1

a)integral^1_0 -7 f(x) dx = -7 integral^1_0 (x - 1) dx = -7 [x^2/2 - x]^1_0 = -7 [1/2 - 1] = -7 [-1/2] b) integral^4_3 2f(x) = 2 integral^4_3 2 dx = 4 integral^4_3 dx = 4 [x]^4_3 = 4 c) integral^7_0 9 f(x) dx = integral^1_0 9 (x - 1) dx + integral^3_1 9 (x - 1) dx + integral^4_3 9 times 2 dx + integral^7_4 9(6 - x)dx = integral^3_0 9 (x - 1) dx + integral^4_3 18 dx + 9 integral^7_4 (6 - x) dx = 9(x^2/2 - x)^3 + 18 (x^4_3 + 9 (6x - x^2/2)^7_4 = 9(9/2 - 3) + 18 + 9 (42 - 49/2) - (24 - 16/2)) = 9 times 3/2 + 18 + 9 (42 - 49/2 - 24 + 8)