How do you graph an integral of f(x) = x?

  • Thread starter courtrigrad
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In summary, graphical integration is a method of finding the area under a curve by drawing a graph of the function and approximating it with geometric shapes. Its main purpose is to solve problems involving rates of change and definite integrals. There are two types: Riemann integration and Trapezoidal integration. The accuracy depends on the number of shapes used and can be improved with more advanced methods. However, it may not provide an exact answer and can be time-consuming for complex functions.
  • #1
courtrigrad
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How would you graph the integral of [tex] f(x) = x [/tex]? What is the process to graph an integral?


Thanks
 
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  • #2
Do you mean to graph this "beauty":
[tex]\int x \ dx =\frac{x^{2}}{2}+C [/tex]

It's a family of parabolas...

Daniel.
 
  • #3
oh ok. thanks a lot
 
  • #4
The way to "graph an integral" is to first find the integral (which will involve a "constant of integration") and then integrate! Since you will have a different function for every value of C, you will, as dextercioby said, a "family" of graphs.
 

1. What is graphical integration?

Graphical integration is a method of finding the area under a curve using graphical representation. It involves drawing a graph of the function and calculating the area under the curve by approximating it with geometric shapes like rectangles or trapezoids.

2. What is the purpose of graphical integration?

The purpose of graphical integration is to find the area under a curve, which has various applications in mathematics, physics, engineering, and other fields. It can also be used to find the values of definite integrals and to solve problems involving rates of change.

3. What are the different types of graphical integration?

There are two main types of graphical integration: Riemann integration and Trapezoidal integration. Riemann integration uses rectangles to approximate the area under the curve, while Trapezoidal integration uses trapezoids. Both methods have their advantages and are used in different situations.

4. How accurate is graphical integration?

The accuracy of graphical integration depends on the number of rectangles or trapezoids used to approximate the area under the curve. The more shapes used, the more accurate the result will be. Additionally, the accuracy can also be improved by using more advanced integration methods, such as Simpson's rule.

5. What are the limitations of graphical integration?

One of the main limitations of graphical integration is that it can only approximate the area under the curve. It may not provide an exact answer, especially for complex functions. Additionally, it can be time-consuming and labor-intensive to draw and calculate the area for a large number of shapes, making it less practical for certain applications.

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