Notice that on a small interval, velocity is approximately constant on subinterval. [(cid:1872) (cid:2869),(cid:1872)] (cid:4666)(cid:1872) (cid:2869)(cid:4667) (cid:4666)(cid:1872)(cid:4667) (cid:4666)(cid:1872) (cid:4667), where (cid:1872) is any point on [(cid:1872) (cid:2869),(cid:1872)]. Class 1a the area and distance problems. Know: area under a velocity vs. time graph gives the total change in position. What is the total distance travelled between 2 and 10s? (cid:1872) (cid:1872) (cid:1872) (cid:2869) (cid:883) (cid:887) Break down [(cid:883),(cid:887)] into places like this: (cid:1872)(cid:2868),(cid:1872)(cid:2869),(cid:1872)(cid:2870), (cid:1872) Note: using midpoints as sample points usually better than using left or right endpoints, but not always. When estimating the distance travelled with right or left sums, smaller rectangles will always result in a better estimation. Sum=same no matter how many rectangles you make it. Suppose that (cid:1858)(cid:4666)(cid:4667) is a decreasing function. total area of (cid:1858) b/w =(cid:1853) and =(cid:1854) left hand (l. s. ) |(cid:1857)(cid:1870)(cid:1870)(cid:1867)(cid:1870) (cid:1866) (cid:1864)(cid:1857)(cid:1858)(cid:1872) (cid:1867)(cid:1870) (cid:1870)(cid:1859) (cid:1872) (cid:1844). (cid:1845). | |(cid:1864)(cid:1857)(cid:1858)(cid:1872) (cid:1844). (cid:1845). (cid:1870)(cid:1859) (cid:1872) (cid:1844). (cid:1845). (cid:1858)(cid:1867)(cid:1870) (cid:1853) (cid:1859)(cid:1857)(cid:1866) (cid:1866)|