Simplification of Integration Problem

  • Context: Undergrad 
  • Thread starter Thread starter mea03wjb
  • Start date Start date
  • Tags Tags
    Integration
Click For Summary
SUMMARY

The discussion centers on the simplification of an integral expressed as the ratio of two separate integrals: y = ∫(1/f(θ, φ)) dφ / ∫(1/g(θ, φ)) dφ. Participants clarify that it is incorrect to combine these integrals into a single integral due to the mathematical properties governing integration. A counterexample using f(x) = x and g(x) = x demonstrates that the result of the ratio of integrals does not equal the integral of the ratio of functions.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with functions and their properties
  • Knowledge of mathematical notation and symbols
  • Basic experience with limits of integration
NEXT STEPS
  • Study the properties of integrals, specifically the linearity of integration
  • Explore counterexamples in integral calculus to solidify understanding
  • Learn about the implications of combining integrals with different functions
  • Investigate advanced integration techniques, such as substitution and integration by parts
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus, as well as educators looking for clarification on integral properties and simplification techniques.

mea03wjb
Messages
6
Reaction score
0
Hi,

I have a problem with an integral - I'd like to simplify it as much as possible...


y =\int\frac{1}{f(theta,phi) }d.phi / \int\frac{1}{g(theta,phi)} d.phi


2 different functions integrated with respect to phi. Note the division symbol between the integrals!

The limits of the integrals are the same so can I just put them in the same integration? Or should I do the integrations separately then divide the end result?

Thanks!
 
Physics news on Phys.org
You most certainly cannot (in general) put them into the same integral. Test it out with a simple case. f(x) = x, g(x) = x. Then int(f)/int(g) = 1, but int(f/g) = int(1) = x.
 

Similar threads

Undergrad Integration Using Trigonometric Substitution
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Integration of √(1-x^2) with x=sinθ: Check Correctness and Simplification
  • · Replies 12 ·
Replies
12
Views
3K
High School Question about the limits of integration in a change of variables
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Substitution in a definite integral
  • · Replies 6 ·
Replies
6
Views
3K
High School Integration by Parts, an introduction I get confused with
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Result of this integral in large Lambda limit
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Landscape Fabric Roll
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad The Euler-Lagrange equation and the Beltrami identity
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Help needed with derivation: solving a complex double integral
  • · Replies 1 ·
Replies
1
Views
2K