area between two curves calculator program

Imagine a farmer trying to sell a piece of land that happens to be perfectly rectangular. The Farmer and his Daughter – Unsold Land The equation for calculating the area of a rectangle is as follows: When the length and width of a rectangle are equal, the shape is a special case of a rectangle, called a square. In the case of a rectangle, the length typically refers to the longer two edges of the quadrilateral, while the width refers to the shorter of the two edges.

A quadrilateral by definition is a polygon that has four edges and vertices. It is one of the simplest shapes, and calculating its area only requires that its length and width are known (or can be measured). RectangleĪ rectangle is a quadrilateral with four right angles. Provided below are equations for some of the most common simple shapes, and examples of how the area of each is calculated. The standard unit of area in the International System of Units (SI) is the square meter, or m 2. It can be visualized as the amount of paint that would be necessary to cover a surface, and is the two-dimensional counterpart of the one-dimensional length of a curve, and three-dimensional volume of a solid. What has been demonstrated is that the same area can be calculated by taking different reference systems and even a reference system can be much easier than the other, in the end it is each one’s decision to use the reference system they want, what matters is to obtain the correct result.Related Surface Area Calculator | Volume CalculatorĪrea is a quantity that describes the size or extent of a two-dimensional figure or shape in a plane. Our first integral will have limits of $-1$ to $2$: This works like this, we are going to need two integrals and what is going to be integrated is going to be the function that is above minus the function that is lower than the area that we want to find. We just need to separate function 1, we will put it as a function $ f (x) $, the part of the function that is above the X-axis will be as follows:Īnd the part of the function that is below the X-axis will look like this:Įverything we just calculated from points of intersections and function 1 that we had to separate into two functions, we will represent in the following figure: Figure 2 Having found the value of $x$ was more than enough, only that as we are going to calculate the area with reference to the Y-axis, we calculate the $y$’s.Ī point that we have not calculated that is very important is the vertex of the parabola of function 1, to calculate it you only have to equal the value of $y$ to zero and we will have the value of $x$: So our points of intersection between the two functions are $(-1,-2)$ and $(2,1)$ We only have to replace each value obtained from $x$: We can easily find the values of $y$ of each point using function 2, which is easier to do calculations than function 1. What gives us as a result that there is a point that has the value of $x = 2$ and the other point has the value of $x = -1$. Once we have the quadratic equation as small as possible, we will factor it to obtain the values of $x$: Multiply that negative sign to the whole parenthesis: Now that we have an equation with only one type of unknown, we proceed to equal it to zero to find the values of $ x $ in which the functions intersect, let’s squared the binomial: To make this calculation we will take the function 1 and its unknown of $y$ we will replace it with the function 2, mathematically it is like this: And the shaded area that is displayed between the functions is the one that will be calculated in this exercise.įirst we are going to calculate the intersection between curves, this calculation is important because it is the one that will define the limits of our integrals.

Area between two curves calculator program