Left Riemann Sum
Right Riemann Sum
Mid-point Riemann Sum
Trapezoidal Sum
100
What is the equation for finding the width between two points? width= ?
(b-a)/n
100
What is the formula for finding the Right Riemann sum?
Area = width*(right height 1 + right height 2 + ... + final height) OR Area of each Rectangle = (base * right height)
100
Which method is most accurate? Midpoint, Right, or Left Riemann?
Midpoint
100
How do you find the area of a trapezoid?
1/2 * height * (base 1 + base 2)
200
If a graph is decreasing, will the left-handed sum create an upper (circumscribed) or lower (inscribed) rectangle?
upper (circumscribed)
200
If a graph is decreasing, will the right-handed sum create an upper (circumscribed) or lower (inscribed) rectangle?
lower (inscribed)
200
How do you find the midpoint between two numbers?
(value 1 + value 2)/2
200
What is the formula for finding the Trapezoidal Sum?
1/2 * width * (height 1 + 2 * height 2 + 2 * height 3 + ... + final height) OR just find the trapezoids separately
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
How do you find the midpoint approximation?
Multiply the width and the y-value found for the x-value in between two other values and repeat for the values over the interval.
300
x: | 1 | 4/3 | 5/3 | 2 | f(x):|9/9|16/9|25/9|36/9| Find the trapezoidal sum for the area of f using three trapezoids over the interval [1,2]
127/54 or 2.352
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
Use four right-handed rectangles of equal width to approximate the area of the region bounded by f(x)=x^2+3 , the x-axis, x=3, and x=5
5-3/4 = 1/2 x: | 3 | 7/2 | 4 | 9/2 | 5 | f(x):|12|61/4|19|93/4|28| area= 1/2 * (61/4+19+93/4+28) answer: 85.5 or 171/2
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
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