Question

5. The Area of a Plane Region. (15 points) a. Find the left Riemann sum for the region bounded by the graph of f(x) = x2 + 2x + 3 and the x-axis between x = 0 and x = 2. (Limit Definition) b. Use Fundamental Theorem of Calculus to solve part a. n с = пс Ži=n(n+1) n(n + 1)(2n +1) 6 =1 i=1 O, O A &

Answer 1

... [x] - [ i, C 2.2 10, [x, x] - [ , 아) C, 2] - [아름, 으+ [2, 73 [ 아 쪽 Date: D 어 3.2 국 Page Na :

(aj let 20-0 X2=0+ 2 X = 0+2 + Y,= 0 + 2 h n-2 n-1 = 0 -2 Xn= n.2 a = 2 X2= 2.2 2 Az = 6-9 Ag = 2-0 h h ch Left hand rule Summation { f(x;) AX ña { $(82)4 Ax Using = 1 n E12 il =) (4-22)-3)? n E .2 ५ ui 3 2 2 h t E 8;2 6 1,7 sul ni 2 8 E th 2 ) h E 6 n ial n² ial n Sulpa (h(hu) (20+ h(h+1) (2n+1) 8 h² hi(n+1) 6 + la 2

8 6 n(n+1) (anti) n² 5(n+1) 6 2 n² 4 3 (11:n) (20))+ 4/1 (143) + 4 lett nyo 4 3 (1) (1) (2)) +46) + 6 + 4+6 + 3 who 10 3 12.66 (6) f(x)= x + 2x + 3 il a polynomial the closed interval [a,b] So its continous apply fundamental theorm of calculus +28+ 3 = 3x 2 3c3 3 +3+3,41 0 O 8 3 4+6 - 12.66