The integral calculator is used to find the antiderivative of any given expression. Limited integral results can also be found by entering bounds. In addition, the area represented by the bounded integral on the function graph is drawn in the graph section. All these operations are done automatically by entering the expression to be integrated, there is no need for any operation other than entering the expression to be integrated and determining the bounds if desired.
The expression to be calculated is written in the upper left “Expression” section. In the lower "Integral" section, the antiderivative is determined, and in the lower "Result" section, the calculated definite integral is calculated. If the bounds are not entered, the upper and lower limits are taken as positive infinity and negative infinity, respectively, and the result is calculated. The area between the graph of the function entered in the graph section on the right and the x-axis is shown in red. The point to be noted here is that the entire area between the x-axis and the function graph is shown in red, and the positive or negative status is not taken into account in the graph. Therefore, numerical estimation from the graph should be avoided unless the areas above and below the x-axis are carefully examined.
Although the integration program can calculate the integral of many functions, there are limits to what it can do. Integral rules are quite a lot and in some complex functions the program is insufficient to find the desired integral.
A definite integral calculation is shown below as an example:
In the above example calculation, x*sin(x)^2 function is integrated. As you can see, it has a very complex antiderivative. Of course, it is possible to simplify this antiderivative quite a bit, but the calculation tool lacks this capability. The result (10.4247) of the bounded integral in the interval (1, 7) can be seen in the lower left. On the right, the area under the function is drawn.