Question

Math 1300: Calculus I Project: Riemann Sums 1. A girl is running at a velocity of 12 feet per second for 10 seconds, as shown in the velocity graph below. v(t) 12 10 6 t 7 10 How far does she travel during this time? This distance can be depicted graphically as a rectangle. Shade such a rectangle and explain why it gives the distance.

Answer 1

Sot Som lo Distance travel -v.t = 12x10 = 120 ft Reclangle width x height t distance = - distance au(t).t 2) Graph ulti-t. Total distance = 12x4+10(7-4)+ 610-7) 48+30+18= 96 ft = - (3) t = 3,6,9,12 Rectangle Area = 3(0(3) tv (6)+v(g) + 4/2)) 376 +9712² = 3 [ 12 135 2 .ft (4.) Each Rutangle width a and height Right 12 ता t 2 4 6 8 10 12 t 2 [u() + v64)+v(6) +0(8) + V110) +222)] +42+6+ +6²+8² +10²t12 2 2 2 [ 10²112² = 1825 12

Isi n = 37 12 width of each re entangle 37 to i. 12 Leight is to 37. 37 Ult) height 37 2 .12 37.12 + 37 131 37².12 total three (v1) rv (25)+(3:13).... +v(37.12 12 cuotas iet les [ +2+3+...+33] 37 ( 37+1) (2.37+1) 37 373 122 = 373 6. 68400 ft 1369 width of each rectangle = 12 6 Right end point of each rectangle 2+2.13+3.42 +--+h12 1.12 2 2 R.12 2. + . (23) 12 12 2 2 List of Area and Sam 12.13 12/m) 12 n + a). +(²13 to.. 12 12 12 + ( 2 ) 12 12 | 12+2 2+2+32 th no

Sum. 7 n(n+1) (anti) het n(n+1) (20+1) n3 8. n=6. 122 416+1) (2.6+) =182 ft (As in 4 same 63 6 3 g lim 122 nlnti) (2n+) h3 from (7) noas 6 lim no 122*3(1+)(2+) > 12 (1+0)(2+0) 6 48 = 6

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