How Do You Calculate the Area Under the Curve f(x) = 9/x from 5 to 10?

  • Context: Undergrad 
  • Thread starter Thread starter mathdum
  • Start date Start date
  • Tags Tags
    Derivative Fraction
Click For Summary
SUMMARY

The area under the curve of the function f(x) = 9/x from the interval [5, 10] can be calculated using its anti-derivative F(x) = 9ln|x|. To find the area, evaluate F at the bounds 10 and 5, resulting in the expression 9ln(10) - 9ln(5). This calculation confirms that the relationship between F(x) and f(x) is that F'(x) = f(x), where F(x) represents the anti-derivative of f(x).

PREREQUISITES
  • Understanding of anti-derivatives and their notation
  • Knowledge of logarithmic functions
  • Familiarity with definite integrals
  • Basic calculus concepts
NEXT STEPS
  • Study the properties of logarithmic functions in calculus
  • Learn how to evaluate definite integrals using anti-derivatives
  • Explore the Fundamental Theorem of Calculus
  • Practice calculating areas under curves for various functions
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus, as well as educators teaching integration techniques.

mathdum
Messages
2
Reaction score
0
Find the area of the region under the graph of the function f on the interval [5, 10].
F(x) = 9/x
 
Physics news on Phys.org
When you say that F(x) = 9/x, do you mean that F'(x) = f(x) where f(x) is the function whose area under its curve you want to calculate? Or did you mistakenly capitalize "f"?
 
Well, my problem just says F(x). Other problems have F'(x), However, this one does not. Hmm...
 
mathdum said:
Well, my problem just says F(x). Other problems have F'(x), However, this one does not. Hmm...

Usually capitalized notation means that it is the anti-derivative. This means you should evaluate F from the given bounds. Do you know how to do this?
 
mathdum said:
Find the area of the region under the graph of the function f on the interval [5, 10].
F(x) = 9/x
Try to be precise in the relationship between F(x) and f(x).
 
9ln|x| + c
 

Similar threads

Undergrad Why split interval here? Area under a curve
  • · Replies 8 ·
Replies
8
Views
2K
High School Integration from "Area Under Curve" Perspective: Explained
  • · Replies 11 ·
Replies
11
Views
2K
MHB -7.64 Determine the following standard normal (z) curve areas:
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Transformation of Functions: How Do Domain and Range Change?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Calculate numerically the area
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Finding the sum of heights under a curve
  • · Replies 3 ·
Replies
3
Views
1K
MHB Which procedure takes the minimum time to solve modulus functions?
  • · Replies 5 ·
Replies
5
Views
1K
MHB Calculating Integral with Simpson's Rule for Error < $0.5\cdot 10^{-3}$
  • · Replies 6 ·
Replies
6
Views
2K
High School Why is this definite integral a single number?
  • · Replies 20 ·
Replies
20
Views
4K
Undergrad How to create a function such that area under curve is 250
  • · Replies 22 ·
Replies
22
Views
3K