Integral Computation with GeoGebra

In today's tutorial, we'll dive into the process of calculating the indefinite integral of a function using GeoGebra, illustrated through a detailed example.

Let's start with the basics: What is an indefinite integral? When we integrate a function, such as f(x), we are essentially finding another function, g(x)+k, $$ \int f(x) = g(x) + k $$ where the derivative D[g(x)+k] brings us back to our original function f(x). $$ D_t[ g(x) + k ] = f(x) $$

Begin by entering a function into GeoGebra. For our demonstration, we'll use the function f(x)=x².

Proceed by using the Integral() command.

Within the command's parentheses, specify the function you're integrating, which we've named "f" for this example.

GeoGebra will then perform the calculation and display the indefinite integral as g(x)=1/3·x³ for the function f(x) we chose.

It's vital to understand that the result of an indefinite integral is not a single function g(x) but rather a family of functions, g(x)+k, where k represents an arbitrary constant. This means a more precise formulation would be g(x)=1/3·x³+k. This principle is based on the fact that the derivative of any constant k is always zero, meaning D[k] = 0. Therefore, derivatives like D[1/3·x³+2] or D[1/3·x³+3] will always revert to the function f(x)=x².

Need confirmation?

Confirm your findings by calculating the derivative using the Derivative() command.

For g(x)=1/3·x³, deriving the first derivative will return us to our starting function f(x)=x², affirming that differentiation serves as the reverse operation of integration.

If you've found this guide enlightening, we encourage you to explore our upcoming tutorials for more insights.