Calculate Integral on Ti 84 Plus

How to Calculate an Integral on TI-84 Plus

Calculating integrals on the TI-84 Plus involves using the built-in integration functions. The calculator can handle both definite and indefinite integrals, making it a valuable tool for students and professionals in mathematics and physics.

To begin, you'll need to understand the basic syntax and steps required to input and solve integrals. The TI-84 Plus provides several methods for integration, including numerical and symbolic approaches.

Step-by-Step Guide

Step 1: Enter the Integral

First, press the MATH key and select option 9: fnInt(. This will bring up the integration function. You'll need to specify the integrand (the function you want to integrate) and the variable of integration.

For example, to integrate \( x^2 \) with respect to \( x \), you would enter:

Step 2: Specify Limits (for Definite Integrals)

If you're calculating a definite integral, you'll need to specify the lower and upper limits. For example, to integrate \( x^2 \) from 0 to 1, you would enter:

Step 3: Execute the Calculation

After entering the integral, press ENTER to execute the calculation. The TI-84 Plus will display the result of the integral.

Worked Example

Let's calculate the definite integral of \( \sin(x) \) from 0 to \( \pi \).

Step 1: Enter the Integral

Press MATH and select fnInt(. Enter the following:

Step 2: Execute the Calculation

Press ENTER. The TI-84 Plus will display the result, which should be approximately 2.

Formula Used

The TI-84 Plus uses numerical integration methods to approximate the value of definite integrals. The general formula for a definite integral is:

Where:

• \( f(x) \) is the integrand
• \( a \) is the lower limit
• \( b \) is the upper limit
• \( \Delta x \) is the width of each subinterval
• \( x_i \) is the midpoint of each subinterval

The TI-84 Plus uses a default number of subintervals (typically 100) to approximate the integral.