how to do indefinite integrals on ti 84

2 min read 16-01-2025

The TI-84 calculator doesn't directly compute indefinite integrals (finding the antiderivative). It excels at definite integrals (finding the area under a curve between limits), but for indefinite integrals, you'll need to use the calculator to assist with the process, not directly solve it. Here's how:

Understanding Indefinite Integrals

Before we dive into calculator usage, let's clarify what an indefinite integral is. Given a function f(x), its indefinite integral, denoted as ∫f(x)dx, represents the family of functions whose derivative is f(x). This family differs by a constant of integration, often represented as "+C".

For example, the indefinite integral of 2x is x² + C, because the derivative of x² + C (for any constant C) is 2x. The TI-84 can't find this "+C", only the core antiderivative.

Using the TI-84 for Assistance with Indefinite Integrals

The TI-84 can help in several ways, primarily by calculating derivatives and providing numerical checks.

1. Using the TI-84 to Verify your Work

This is the most practical use. Once you've manually calculated an indefinite integral, use the calculator's numerical derivative feature to check your answer.

Manually compute the integral: Let's say you've integrated 3x² and got x³ + C.
Use the nDeriv function: The TI-84 Plus CE has a built-in numerical derivative function (nDeriv). Access it by pressing MATH then scrolling down to nDeriv(.
Input your answer: Enter nDeriv(x^3,x,x) (this calculates the derivative of x³ with respect to x, at the point x). The calculator should return 3x², confirming your integral is correct. Remember, the '+C' disappears when taking the derivative.
Important Note: nDeriv provides an approximation of the derivative. For simple functions, it's highly accurate, but for complex ones, the approximation might not be perfect.

2. Using the TI-84 for Definite Integrals (Related to Indefinite Integrals)

While not directly finding the indefinite integral, solving definite integrals helps understand the concept. The Fundamental Theorem of Calculus links definite and indefinite integrals: the definite integral from a to b of f(x) is F(b) - F(a), where F(x) is the indefinite integral of f(x).

Use the fnInt function: This is found under the MATH menu. It calculates definite integrals. For example, fnInt(3x^2,x,0,2) calculates the definite integral of 3x² from x=0 to x=2.
Connect to the indefinite integral: You manually find the indefinite integral (x³ + C), then use the Fundamental Theorem to get the definite integral: (2³ + C) - (0³ + C) = 8. The calculator's fnInt function should give the same result.

3. Using Symbolic Math Software (Not the TI-84)

For direct calculation of indefinite integrals, you'll need more powerful software such as:

Wolfram Alpha: A free online tool that can compute symbolic integrals. Just type in your function (e.g., "integrate 3x^2 dx").
TI-Nspire CAS: This calculator (more advanced than the TI-84) has Computer Algebra System capabilities that allow symbolic integration.

Conclusion

The TI-84 calculator isn't designed for symbolic indefinite integration. However, its numerical derivative and definite integral functions are invaluable tools for checking your manually computed indefinite integrals and reinforcing your understanding of the Fundamental Theorem of Calculus. For direct symbolic integration, utilize specialized software like Wolfram Alpha or a CAS calculator.