Helping a 5-Year-Old Integrate a Function in Kindergarten

  • Context: High School 
  • Thread starter Thread starter docnet
  • Start date Start date
  • Tags Tags
    Function Integrate
Click For Summary
SUMMARY

The discussion focuses on integrating a function over the boundary of the first quadrant, specifically denoted as ##\partial \Omega##. The boundary is defined as ##\partial\Omega = \{ x=0, y\geq 0 \} ∪ \{ x\geq 0, y=0 \}##. The correct integral representation is given by $$\int_{\partial\Omega} f(x,y) dS$$, which can be expressed as $$\int^\infty_0 f(x,0) dx + \int^\infty_0 f(0,y) dy$$. To simplify the explanation for a five-year-old, it is suggested to switch the order of the integrals to align with the boundary's definition.

PREREQUISITES
  • Basic understanding of calculus, specifically integration.
  • Familiarity with the concept of boundaries in multivariable functions.
  • Knowledge of function notation and evaluation.
  • Understanding of the first quadrant in Cartesian coordinates.
NEXT STEPS
  • Explore the fundamentals of multivariable calculus, focusing on integration techniques.
  • Study the properties of boundaries in calculus, particularly in relation to regions in the Cartesian plane.
  • Learn about changing the order of integration in double integrals.
  • Investigate how to explain complex mathematical concepts to young children effectively.
USEFUL FOR

Parents, educators, and tutors who are assisting young children with early mathematics projects, particularly those involving basic calculus concepts.

docnet
Messages
796
Reaction score
486
TL;DR
what is the rule for integration along two lines that meet at an angle?
A newbie who knows basic math is helping a five year old do his kindergarten project. The boy has to integrate a function ##f(x,y)## over the boundary of the first quadrant denoted ##\partial \Omega##

where ##\partial\Omega = \{ x=0, y\geq 0 \} ∪ \{ x\geq 0, y=0 \} ##

How would I explain to this five year old how to integrate this?

$$\int_{\partial\Omega} f(x,y) dS $$
is this right?

$$\int^\infty_0 f(x,0) dx + \int^\infty_0 f(0,y) dy$$
 
Physics news on Phys.org
It looks right to me. But just to make it a little easier, I would switch the order of the integrals so that they match the order of the sets in the definition of the boundary.
 
  • Informative
Likes   Reactions: docnet

Similar threads

  • · Replies 21 ·
Replies
21
Views
2K
  • · Replies 21 ·
Replies
21
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 19 ·
Replies
19
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 1 ·
Replies
1
Views
2K