MHB Real World Apps of Improper Integrals: Impact & Syllabus

  • Thread starter Thread starter matqkks
  • Start date Start date
  • Tags Tags
    Integration
Click For Summary
Improper integrals are crucial in real-world applications, particularly in statistics for calculating probabilities on the normal curve. They are essential in hypothesis testing, where determining the probability of a value being above a certain threshold involves integrating from a point to infinity. This concept is foundational in calculus, which is why it appears on syllabi for introductory courses. Understanding improper integrals enhances comprehension of areas under curves and limits, which are vital in various fields. Their practical significance in statistics and probability underscores their importance in education.
matqkks
Messages
280
Reaction score
5
What are the real life applications of improper integrals? Why are they on the syllabus of every first course in calculus?
I am looking for examples which have a real impact.
 
Physics news on Phys.org
matqkks said:
What are the real life applications of improper integrals? Why are they on the syllabus of every first course in calculus?
I am looking for examples which have a real impact.

My area of interest is primarily statistics and although we don't do these by hand at all, improper integrals are used all the time when calculating probabilities on the normal curve. In hypothesis testing we often ask what is the probability something is at least some value... this in essence is asking to take an integral from $[a,\infty]$.
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
View full post »

Similar threads

Improper Integrals: Real-Life Applications & Syllabus Impact
  • · Replies 1 ·
Replies
1
Views
4K
What are some tips for succeeding in Calculus II?
  • · Replies 4 ·
Replies
4
Views
2K
B Explain Integration to me, please
  • · Replies 5 ·
Replies
5
Views
2K
I How does the limit comparison test for integrability go?
  • · Replies 2 ·
Replies
2
Views
1K
I Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
1K
MHB Evaluating Improper Integrals: Convergence or Divergence?
  • · Replies 3 ·
Replies
3
Views
2K
Is this result trivial? (improper integral representations of real functions))
  • · Replies 8 ·
Replies
8
Views
2K
B How can hyperreal numbers make infinitesimals logically sound in calculus?
  • · Replies 24 ·
Replies
24
Views
6K
I Munkres-Analysis on Manifolds: Extended Integrals
  • · Replies 5 ·
Replies
5
Views
2K
A Integrating a function of which poles appear on the branch cut
  • · Replies 1 ·
Replies
1
Views
2K