# How to Calculate Integrals with a TI-83 Plus Graphing Calculator

Integrals are mathematical ideas used in generalizing the area of a graph or the volume of a three-dimensional object. Understanding integrals is a key part of calculus. They are a tenet in the fields of math, statistics, engineering and science. Knowing how to calculate integrals gives anyone working in or studying these fields a core foundation to expand on. Building that core foundation is hard if you do not know how to use a calculator to calculate integrals. However, a simple explanation of the process can make integrals an easy calculation.

### Things You'll Need

- TI-83 Plus graphing calculator

#### Step 1

Open the "Y=" menu of the calculator. It is a light purple button on the left-hand side of the calculator, just below the screen.

#### Step 2

Graph the curve, "y=f(x)." For this solution to work, the curve will need to be on an interval that contains "x" as more than or equal to "a," but less than or equal to "b."

#### Step 3

Press the "2nd" button. It is dark yellow and on the upper-left corner of the keypad.

#### Step 4

Press the "Trace" button. It is purple and just below the calculator screen, three buttons to the right of the "Y=" button. Because we pressed "2nd" first, we are actually opening the menu of "Calc."

#### Step 5

Select option number seven. This option will integrate a function between two endpoints.

#### Step 6

Reply to the calculator with "a" when it asks on the bottom of the screen for the "Lower Limit."

#### Step 7

Press "Enter," located on the bottom right of the keypad. The calculator will immediately ask for the value of the "Upper Limit."

#### Step 8

Respond by selecting "b."

#### Step 9

Press "Enter" again.

#### Step 10

Look on the bottom of the screen and you will see the calculation of the integral.

### Tips & Warnings

- The region between the graph of y=f(x) and the x-axis, shaded by the calculator, is a visual representation of the integral.
- A calculation can work without any of the graph visible on the screen; you will not need to rearrange the view.
- Trying this on any calculator other than a TI-83 or TI-83 Plus will not work. Each calculator model is different.
- Make sure when you press in your "Upper Limit" and "Lower Limit" values that they are correct. A wrong stroke on the keypad can cause results to be wrong.