Consider f(x) = 12 on the interval [3,7]. (a) (1) Estimate the area under the graph of f(x) using 8 approximating rectangles and left endpoints (as illustrated in the graph below). Area 2 (ii) This Riemann sum is an ? (b) (1) Estimate the area under the graph of f(x) using 8 approximating rectangles and right endpoints (as illustrated in the graph below). Area 2 (ii) This Riemann sum is an ? (Click on each graph to open in a new window.)
Consider f(x) = 12 on the interval [3,7]. (a) (1) Estimate the area under the graph of f(x) using 8 approximating rectangles and left endpoints (as illustrated in the graph below). Area 2 (ii) This Riemann sum is an ? (b) (1) Estimate the area under the graph of f(x) using 8 approximating rectangles and right endpoints (as illustrated in the graph below). Area 2 (ii) This Riemann sum is an ? (Click on each graph to open in a new window.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Question
![8
8
7
7
6
4
4
3
1
3 4 5
6
8
4 5
6
7
2 on [3, 7]
12
(b) Right endpoint Riemann sum for y =
2 on [3, 7]
(a) Left endpoint Riemann sum for y =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb406efe-69ee-4086-9eb7-bd1c9f2049b1%2F22a66e68-6145-480f-b94b-31fdf6aaa023%2Fhi902si_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8
8
7
7
6
4
4
3
1
3 4 5
6
8
4 5
6
7
2 on [3, 7]
12
(b) Right endpoint Riemann sum for y =
2 on [3, 7]
(a) Left endpoint Riemann sum for y =
![Consider f(x)
12
on the interval [3,7].
(a) (1) Estimate the area under the graph of f(x) using 8 approximating rectangles and left endpoints (as illustrated in the
graph below).
Area 2
(ii) This Riemann sum is an
(b) (1) Estimate the area under the graph of f(x) using 8 approximating rectangles and right endpoints (as illustrated in the
graph below).
Area 2
(ii) This Riemann sum is an
?
(Click on each graph to open in a new window.)
7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb406efe-69ee-4086-9eb7-bd1c9f2049b1%2F22a66e68-6145-480f-b94b-31fdf6aaa023%2Fpba0jp9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider f(x)
12
on the interval [3,7].
(a) (1) Estimate the area under the graph of f(x) using 8 approximating rectangles and left endpoints (as illustrated in the
graph below).
Area 2
(ii) This Riemann sum is an
(b) (1) Estimate the area under the graph of f(x) using 8 approximating rectangles and right endpoints (as illustrated in the
graph below).
Area 2
(ii) This Riemann sum is an
?
(Click on each graph to open in a new window.)
7
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