# How to Graph Antiderivatives on the TI-Nspire

A function has an infinite number of antiderivatives. In the example given here, you look at a particular antiderivative on the TI-Nspire and then see how to use a slider to investigate an entire family of curves defined by an antiderivative.

## Use the TI-Nspire definite integral template

To graph the antiderivative of *y* = *x*^{3} – 3*x*^{2} – 2*x* + 6, follow these steps:

Press [CTRL][G] to open the entry line, then graph

*y*=*x*^{3}– 3*x*^{2}– 2*x*+ 6.Press

**to open the Math template, highlight the definite integral template, and press [ENTER].**See the first screen.

Press [0] to input the lower limit of the definite integral template, and then press [TAB] to move to the upper-limit field. Press [X] and then press [TAB] to move to the integral field.

Type f1(

*x*) or press**[VAR]**and select f1 from the list of variables, then press**[TAB]**again to move to the next field of the definite integral template.Type

*x*in the last field and press [ENTER] to graph the antiderivative.It may take a few seconds for the graph to form on a handheld.

The antiderivative that is graphed here is defined by the equation *y* = 1/4*x*^{4} – *x*^{3} – *x*^{2} – 6*x*.

This equation is based on the general solution *y* = 1/4*x*^{4} – *x*^{3} – *x*^{2} – 6*x** *+ *C *with *C* = 0.

## Use the indefinite integral template on TI-Nspire CAS

You can also use TI-Nspire CAS to graph this antiderivative using the indefinite integral template, also found in the Math template accessed by pressing

To add a dynamic element, try inserting a slider defined by the variable *c*. As shown in the first screen, use the definite integral template to graph the antiderivative as before. Then add + *c* in the equation for the purpose of investigating the family of curves given by the antiderivative of *y* = *x*^{3} – 3*x*^{2} – 2*x* + 6.

Right-click the slider and change the settings to Minimized (see the second screen).** **As you see in the last screen, you can click the slider and watch the graph of the derivative translate vertically.