What is the area between the curve y=\sqrt{1-x} and the coordinate axes?

In summary, to find the area between the curve y=\sqrt{1-x} and the coordinate axes, one must perform the integral \int_{0}^{1}\sqrt{1-x}dx by using the substitution u=1-x. This is because the x-intercept of the curve is 1, and the area can be found by taking the modulus of the integral.
  • #1
tandoorichicken
245
0
Find the are between the curve [tex] y=\sqrt{1-x} [/tex] and the coordinate axes
 
Physics news on Phys.org
  • #2
Do you know integral calculus?
 
  • #3
I think it would be f(max) - f(min) where f(x) = (2/3)(1 - x)^(3/2)
 
  • #4
You have to perform the integral
[tex]\int_{0}^{1}\sqrt{1-x}dx[/tex]
Try the substitution u=1-x
 
  • #5
First find the domain and range that will give u limits of integration


Why you need a substitution

[tex]\int_{0}^{1}\sqrt{1-x}d(1-x)[/tex]
 
  • #6
Originally posted by himanshu121

Why you need a substitution

[tex]\int_{0}^{1}\sqrt{1-x}d(1-x)[/tex]
I do believe this integral is equivalent to the one I posted. But how does your integral follow from the problem?
 
  • #7
I was just shortening the step which are required for substitutions

Anyway i will be thinking that way too which u have asked
 
  • #8
In order to do this problem, we usually take the following steps.
1. Sketch the curve [tex] y=\sqrt{1-x} [/tex] and find out what exactly you need to find.

2. Find the x-intercept(s) or y-intercept(s).

3. Write down a definite integral and solve the problem.

In this case, the x-intercept is 1, so you can find out the area by [tex]\int_{0}^{1}\sqrt{1-x}dx[/tex]

Originally posted by himanshu121
[tex]\int_{0}^{1}\sqrt{1-x}d(1-x)[/tex]
It should be
[tex]-\int_{0}^{1}\sqrt{1-x}d(1-x)[/tex]
 
  • #9
Area is positive so in any case it is modulus
of the integral
 

1. What is the area between a curve and the axes?

The area between a curve and the axes is the region enclosed by the curve and the x and y axes on a graph. It is often referred to as the "shaded area" or the "area under the curve."

2. How do you calculate the area between a curve and the axes?

To calculate the area between a curve and the axes, you can use integration. First, find the points of intersection between the curve and the axes. Then, integrate the function from one point to the other to find the area. If the curve lies above the x-axis, the area will be positive. If the curve lies below the x-axis, the area will be negative.

3. Can the area between a curve and the axes be negative?

Yes, the area between a curve and the axes can be negative if the curve lies below the x-axis. This indicates that the curve is actually subtracting from the total area rather than adding to it.

4. What is the significance of finding the area between a curve and the axes?

Finding the area between a curve and the axes is important in many fields of science and mathematics. It can be used to calculate distances, volumes, and probabilities. It is also a fundamental concept in calculus and is often used in physics, engineering, and economics.

5. Can the area between a curve and the axes be approximated without integration?

Yes, the area between a curve and the axes can be approximated using numerical methods such as Riemann sums or the trapezoidal rule. These methods divide the area into smaller sections and use basic geometry to estimate the total area. However, as the number of sections increases, the approximation becomes more accurate and approaches the actual area calculated through integration.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
691
  • Introductory Physics Homework Help
Replies
26
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
561
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
144
  • Introductory Physics Homework Help
Replies
9
Views
791
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
168
  • Introductory Physics Homework Help
Replies
6
Views
1K
Back
Top