- #1
tandoorichicken
- 245
- 0
Find the are between the curve [tex] y=\sqrt{1-x} [/tex] and the coordinate axes
I do believe this integral is equivalent to the one I posted. But how does your integral follow from the problem?Originally posted by himanshu121
Why you need a substitution
[tex]\int_{0}^{1}\sqrt{1-x}d(1-x)[/tex]
It should beOriginally posted by himanshu121
[tex]\int_{0}^{1}\sqrt{1-x}d(1-x)[/tex]
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."
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.
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.
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.
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.