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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please help
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
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
