Integration Review Part I When you see the words… This is what you think of doing…  A Riemann Sum equivalent to the definite integral is… -- 1.

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Presentation transcript:

Integration Review Part I When you see the words… This is what you think of doing…  A Riemann Sum equivalent to the definite integral is… -- 1

Integration Review Part I When you see the words… This is what you think of doing…  If f is continuous and bounded on an interval containing x = a and  F’(x) = f(x) for all x in the interval 2

Integration Review Part I When you see the words… This is what you think of doing…  F (b) – F(a) where F’ = f 3

Integration Review Part I When you see the words… This is what you think of doing… -- 4

Integration Review Part I When you see the words… This is what you think of doing… -- 5

Integration Review Part I When you see the words… This is what you think of doing…  f(x) 6

Integration Review Part I When you see the words… This is what you think of doing…  f( g(x) ) * g’(x) 7

Integration Review Part I When you see the words… This is what you think of doing… 00 8

Integration Review Part I When you see the words… This is what you think of doing… Trapezoid Rule -- 9

Integration Review Part I When you see the words… This is what you think of doing… If f is increasing on the interval [a,b], then a Left Riemann Sum (overestimates, underestimates) the true value of  Underestimates 10

Integration Review Part I When you see the words… This is what you think of doing… If f is decreasing on the interval [a,b], then a Left Riemann Sum (overestimates, underestimates) the true value of  Overestimates 11

Integration Review Part I When you see the words… This is what you think of doing… If f is increasing on the interval [a,b], then a Right Riemann Sum (overestimates, underestimates) the true value of  Overestimates 12

Integration Review Part I When you see the words… This is what you think of doing… If f is decreasing on the interval [a,b], then a Right Riemann Sum (overestimates, underestimates) the true value of  Underestimates 13

Integration Review Part I When you see the words… This is what you think of doing… If f is concave upward on the interval [a,b], then the Midpoint Riemann Sum (overestimates, underestimates) the true value of  Underestimates 14

Integration Review Part I When you see the words… This is what you think of doing… If f is concave downward on the interval [a,b], then the Midpoint Riemann Sum (overestimates, underestimates) the true value of  Overestimates 15

Integration Review Part I When you see the words… This is what you think of doing… If f is concave downward on the interval [a,b], then the Trapezoid Rule Sum (overestimates, underestimates) the true value of  Underestimates 16

Integration Review Part I When you see the words… This is what you think of doing… If f is concave upward on the interval [a,b], then the Trapezoid Rule Sum (overestimates, underestimates) the true value of  Overestimates 17

Integration Review Part I When you see the words… This is what you think of doing… Displacement (Integral) .. 18

Integration Review Part I When you see the words… This is what you think of doing… .. 19

Integration Review Part I When you see the words… This is what you think of doing… .. 20

Integration Review Part I When you see the words… This is what you think of doing… .. 21

Integration Review Part I When you see the words… This is what you think of doing… .. 22