How to Find the Area Between Two Curves and Their Intersection Points

  • Thread starter Thread starter curlyq0987
  • Start date Start date
  • Tags Tags
    Area Curves
Click For Summary
SUMMARY

The discussion focuses on calculating the area between the curves defined by the equations y=4xe^-x^2 and y=|x|, specifically between the intersection points at x=0 and x=√(-ln(1/4)). The area under the curve y=4xe^-x^2 from x=0 to x=√(-ln(0.25)) and the area under y=|x| over the same interval are the primary calculations discussed. The user initially faced challenges but resolved them with further understanding and assistance from the community.

PREREQUISITES
  • Understanding of calculus, specifically integration techniques.
  • Familiarity with exponential functions and absolute value functions.
  • Knowledge of finding intersection points of curves.
  • Ability to evaluate definite integrals.
NEXT STEPS
  • Study integration techniques for calculating areas between curves.
  • Learn about the properties of exponential functions and their graphs.
  • Explore methods for finding intersection points of complex functions.
  • Practice evaluating definite integrals using various functions.
USEFUL FOR

Students and educators in calculus, mathematicians, and anyone interested in advanced integration techniques and the analysis of functions.

curlyq0987
Messages
2
Reaction score
0
1. Find the area between the curves y=4xe^-x^2, y=abs(x)


2. intersection points are 0 and sqrt(-ln(1/4))



3. help!
 
Physics news on Phys.org
Well what is the area under

y=4xe-x2 between x=0 and x=√(-ln(0.25)) ?

Then find the area under the graph of y=|x| from x=0 to x=√(-ln(0.25)).

No what do you think you should do?
 
I actually figured it out shortly after posting this. I was making some really dumb mistakes! But thank you for replying so quickly. I'm sure I'll be back soon needing some more help :)
 

Similar threads

Find the area delimited by two polar curves
  • · Replies 2 ·
Replies
2
Views
2K
Calculating Area Under a Curve Using Change of Variables and Quotient Rule
  • · Replies 5 ·
Replies
5
Views
2K
Integration problem using inscribed rectangles
  • · Replies 14 ·
Replies
14
Views
2K
Understanding First Order ODEs and Intersection of Curves
  • · Replies 4 ·
Replies
4
Views
2K
Area of segment cut from a circle
  • · Replies 2 ·
Replies
2
Views
2K
Generalisations of area between two curves
  • · Replies 59 ·
2
Replies
59
Views
5K
Simple integration to find area
  • · Replies 2 ·
Replies
2
Views
2K
Area surface of revolution (rotating this astroid curve around the x-axis)
  • · Replies 2 ·
Replies
2
Views
2K
Find all points of intersection
  • · Replies 6 ·
Replies
6
Views
2K
Finding Area of Shaded Segment in Circle Using Calculus
  • · Replies 6 ·
Replies
6
Views
2K