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

In summary, the area between two curves is the region enclosed by two curves on a graph, representing the space between the two curves and the x-axis. To calculate it, you need to find the points of intersection between the two curves and use the definite integral. It can be negative if one curve lies below the other, and it is significant in various fields of math and science. However, there are limitations, such as the curves needing to be continuous and not intersecting more than twice in the given interval.
  • #1
curlyq0987
2
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
  • #2
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?
 
  • #3
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 :)
 

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

What is the area between two curves?

The area between two curves is the region enclosed by two curves on a graph. It is the space between the two curves and the x-axis.

How do you calculate the area between two curves?

To calculate the area between two curves, you need to find the points of intersection between the two curves. Then, you can use the definite integral to find the area between those points of intersection.

Can the area between two curves be negative?

Yes, the area between two curves can be negative if one curve lies below the other curve. This means that the integral will have a negative value, indicating a negative area.

What is the significance of finding the area between two curves?

The area between two curves is important in many areas of mathematics and science. It can represent the total value of a function, the displacement of an object, or the amount of work done in a system.

Are there any limitations to finding the area between two curves?

Yes, there are limitations to finding the area between two curves. One limitation is that the curves must be continuous and have a finite area. Additionally, the curves must not intersect more than twice in the given interval.

Similar threads

Find the area delimited by two polar curves
Replies
2
Views
1K
Calculating Area Under a Curve Using Change of Variables and Quotient Rule
Replies
5
Views
2K
Integration problem using inscribed rectangles
Replies
14
Views
1K
Understanding First Order ODEs and Intersection of Curves
Replies
4
Views
1K
Generalisations of area between two curves
2
Replies
59
Views
4K
Simple integration to find area
Replies
2
Views
1K
Finding Area of Shaded Segment in Circle Using Calculus
Replies
6
Views
1K
Find all points of intersection
Replies
6
Views
1K
Area between 2 curves, Volume around X and Y, Centroid
Replies
1
Views
2K
Values of c for which quartic curve intersects a line
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top