Left Riemann Sum
Right Riemann Sum
Mid-point Riemann Sum
Trapezoidal Sum
Summation Notation
100
What is the equation for finding the width between two points?
width= ?
(b-a)/n
100
What f(x) do you leave off in the table when calculating a right reimann sum.
The furthest left f(x)
100
Which method is most accurate? Midpoint, Right, or Left Riemann?
Midpoint
100
How do you find the area of a trapezoid?
h x (b1 + b2 )/2
100
9
Σ i
i=2
44
200
If a graph is decreasing, will the left-handed sum create an overestimate or underesimate.
overestimate
200
If a graph is decreasing, will the right-handed sum create an overestimate or an underestimate?
underestimate
200
How do you find the midpoint between two numbers?
(value 1 + value 2)/2
200
What is the formula for Trianglular sum?
1/2 b x h
200
8
Σ 2i+4
i=1
104
300
x: | 0 | 1 | 2 | 3 | 4 | f(x):|20|18 |17|11| 3 | Use Left-handed rectangles with four subintervals to estimate the area on the interval [0,4]
66
300
x: | 2 | 4 | 6 | 7 | 8 |
f(x):| 3 | 7 |10|13|15|
Use right-handed rectangles to estimate the area with four subintervals for f on the interval [2,8]
area= 2(7)+2(10)+1(13)+1(15)
answer: 62
300
x: | 0 | 1 | 2 | 3 | 4 | f(x):|20|18 |17|11| 3 | Use midpoint sum with four subintervals to estimate the area on the interval [0,4]
57.5
300
12.5
300
6
Σ n2
n=1
91
400
x: | 0 | 2 | 5 | 10 | f(x): | 1 | 3 | 9 | 30 | Use Left-handed rectangles with three subintervals to estimate the area on the interval [0,10]
56
400
Find the area if x: | 3 | 7/2 | 4 | 9/2 | 5 | and f(x):|12|61/4|19|93/4|28| using a right reimann sum.
42.75
400
x: | 2 | 4 | 6 | 7 | 8 | f(x):| 3 | 7 |10|13|15| Give the midpoint approximation with two subintervals for f on the intervals [2,8]
=4(7)+2(13) answer: 54
400
x: | 2 | 5 | 7 | 8 | f(x): |10|30|40|20| Find the trapezoidal approximation of the function f over the closed interval [2,8]
160
400
Write the expression in summation notation for the series (3 + 5 +7 + 9)
4
Σ 2i+1
i=1