Beginner Integration: Intg'g Arbitrary Funcs: Area B/w Intersects

Click For Summary
SUMMARY

The discussion focuses on calculating the area between two intersecting functions using integration, specifically addressing the scenario where one function, such as sin(x), intersects another arbitrary function. The integral is defined as ∫a to b f(x)dx=F(b)-F(a). Participants confirm that to find the area between the curves, one must perform two separate integrations: one for the function below the intersection and another for the function above it. This method ensures accurate calculation of the area between the curves and the x-axis.

PREREQUISITES
  • Understanding of definite integrals and the Fundamental Theorem of Calculus
  • Familiarity with the properties of functions and their intersections
  • Knowledge of integration techniques for different types of functions
  • Basic skills in graphing functions to visualize intersections
NEXT STEPS
  • Study the Fundamental Theorem of Calculus in detail
  • Learn about numerical integration methods for complex functions
  • Explore graphical methods for finding intersections of functions
  • Investigate applications of integration in calculating areas between curves
USEFUL FOR

Mathematics students, educators, and anyone interested in advanced calculus concepts, particularly those focusing on integration and area calculations between curves.

Jake Minneman
Messages
24
Reaction score
0
http://www.google.com/imgres?imgurl=http://www.msstate.edu/dept/abelc/math/integral_area.png&imgrefurl=http://www.msstate.edu/dept/abelc/math/integrals.html&usg=__eYIUnirereMFeYOxrfWSZ22D6MU=&h=599&w=684&sz=24&hl=en&start=0&sig2=5Xoc8E51gnWrd4Z6mnluLA&zoom=1&tbnid=ofF46QkIclKjQM:&tbnh=142&tbnw=162&ei=7VfZTbHvDdO_gQfe49lX&prev=/search%3Fq%3Ddefinition%2Bof%2Ban%2Bintegral%26um%3D1%26hl%3Den%26sa%3DN%26biw%3D1416%26bih%3D1071%26tbm%3Disch&um=1&itbs=1&iact=rc&dur=520&sqi=2&page=1&ndsp=44&ved=1t:429,r:22,s:0&tx=106&ty=50
I know this to be the definition of an integral in the form of
∫a to b f(x)dx=F(b)-F(a)
But what if, however, there were another arbitrary function intersecting the function in the picture twice each with a curved nature. For example the function sin(x) is it possible buy using integration to calculate the area in between the two intersection points and the x-axis
Kind of a strange question, and its not very to the point ask questions if you do not understand my wording.
 
Physics news on Phys.org
Hi Jake! :smile:

You mean the area under the lower of two intersecting functions?

Just do two integrations, one for the first function when it's underneath, the other for the second function when it's underneath. :wink:
 
Yes exactly, thank you very much.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 1 ·
Replies
1
Views
4K
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
7K
  • · Replies 4 ·
Replies
4
Views
2K