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Math 1300: Calculus I Project: Riemann Sums 1. A girl is running at a velocity of 12 feet per second for 10 seconds, as shown2. Now the girl changes her velocity as she runs. Her velocity graph is approximately as shown: v(t) 12 10 6 4. 10 How far do3. This time she starts off slowly and speeds up. 12 V 12 The velocity is given by v(t) = (time in seconds, velocity in ft/se4. Now, for the same velocity function v(t) = fə, get a better estimate of how far she travelled using n= 6 rectangles. Draw37 rectangles. Use fractions, not 5. Now we will estimate the area when there are n decimals. (a) Width of each rectangle: (b6. Now we will figure out the estimate when there are an arbitrary number of rectangles, or n rectangles. (a) Width of each r7. Manipulate the sum algebraically until it is of the form: stuff. (1+4+9+ ... + n). n(n+1)(2n + 1) 8. Simplify further by s9. As n approaches infinity we find her exact distance travelled (the exact area under the curve). Take the limit as n goes t

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(1) A girl is running at a velocity of 12 feet per second for 10 seconds, as shown in the velocity graph below Vit) 12 ht lo

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