Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Learning Goal: To understand the concept of an integral as the area under a Figure a The function y=f(x)/ Ar b 4 of 4 Now, look at a general function f(x), as shown in (Figure 4). Suppose you want to find the area under the curve, between x = a and x = b-that is, the blue shaded area. Using our method above, we can add up the areas of lots of skinny rectangles like the green one. Each rectangle has area f(x)Ax, and we want to sum these areas between x = a and x = b, letting Ax get very small. Mathematically, you may recognize this sum as a definite integral: f(x) dx. The notation may look intimidating, but just keep in mind that the f(x)da refers to the small rectangle areas, the sign stands, in a sense, for the S in "sum" (that's actually how the symbol for integration was chosen), and the a and b at the bottom and top of give you the start and end of the region you're interested in. Thus, the definite integral få f(x) dx means the total area under the curve f(x) between x = a and x = b. For the function f(2) shown below, find the definite integral i f(x) dx. Express your answer numerically. f(x) 6 4 2 0 0 1 2 3 4

Learning Goal: To understand the concept of an integral as the area under a Figure a The function y=f(x)/ Ar b 4 of 4 Now, look at a general function f(x), as shown in (Figure 4). Suppose you want to find the area under the curve, between x = a and x = b-that is, the blue shaded area. Using our method above, we can add up the areas of lots of skinny rectangles like the green one. Each rectangle has area f(x)Ax, and we want to sum these areas between x = a and x = b, letting Ax get very small. Mathematically, you may recognize this sum as a definite integral: f(x) dx. The notation may look intimidating, but just keep in mind that the f(x)da refers to the small rectangle areas, the sign stands, in a sense, for the S in "sum" (that's actually how the symbol for integration was chosen), and the a and b at the bottom and top of give you the start and end of the region you're interested in. Thus, the definite integral få f(x) dx means the total area under the curve f(x) between x = a and x = b. For the function f(2) shown below, find the definite integral i f(x) dx. Express your answer numerically. f(x) 6 4 2 0 0 1 2 3 4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Please help

Learning Goal: To understand the concept of an integral as the area under a Figure a The function y=f(x)/ Ax < 4 of 4 b Now, look at a general function f(x), as shown in (Figure 4). Suppose you want to find the area under the curve, between x = a and x = b-that is, the blue shaded area. Using our method above, we can add up the areas of lots of skinny rectangles like the green one. Each rectangle has area f(x)Ax, and we want to sum these areas betweenx = a and x = b, letting Ax get very small. Mathematically, you may recognize this sum as a definite integral: f(x) dx. The notation may look intimidating, but just keep in mind that the f(x)da refers to the small rectangle areas, the sign stands, in a sense, for the S in "sum" (that's actually how the symbol for integration was chosen), and the a and b at the bottom and top of a give you the start and end of the region you're interested in. Thus, the definite integral f f(x) dx means the total area under the curve f(x) between a = a and x = b. For the function f(x) shown below, find the definite integral f₁ f(x) dx. Express your answer numerically. f(x) 6 4 2 0 0 1 2 3 4 5 X
Transcribed Image Text:Learning Goal: To understand the concept of an integral as the area under a Figure a The function y=f(x)/ Ax < 4 of 4 b Now, look at a general function f(x), as shown in (Figure 4). Suppose you want to find the area under the curve, between x = a and x = b-that is, the blue shaded area. Using our method above, we can add up the areas of lots of skinny rectangles like the green one. Each rectangle has area f(x)Ax, and we want to sum these areas betweenx = a and x = b, letting Ax get very small. Mathematically, you may recognize this sum as a definite integral: f(x) dx. The notation may look intimidating, but just keep in mind that the f(x)da refers to the small rectangle areas, the sign stands, in a sense, for the S in "sum" (that's actually how the symbol for integration was chosen), and the a and b at the bottom and top of a give you the start and end of the region you're interested in. Thus, the definite integral f f(x) dx means the total area under the curve f(x) between a = a and x = b. For the function f(x) shown below, find the definite integral f₁ f(x) dx. Express your answer numerically. f(x) 6 4 2 0 0 1 2 3 4 5 X
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS