Final answer:
Definite integration (Option D) is the calculator function that computes definite integrals step by step. Other options, like indefinite integration, Riemann sum approximation, and Simpson's rule, are different approaches to integration and estimating integrals, but the direct calculation is performed by the definite integration function on calculators. Option D is the correct answer.
Step-by-step explanation:
The function that computes definite integrals step by step is identified in the question options. Here's how each option relates to definite integration:
- Indefinite integration (Option A) does not calculate definite integrals from one point to another, but rather finds the general form of the antiderivative of a function.
- Riemann sum approximation (Option B) provides a method for estimating the definite integral, using sums of areas of rectangles.
- Simpson's rule application (Option C) is another numerical method for estimating definite integrals, which is more accurate than the Riemann sum for smooth functions.
- Definite integration (Option D) calculates the integral of a function within given limits, providing the exact area under the curve from one point to another.
Calculators such as the TI-83, 83+, or 84 series have built-in functions to compute definite integrals. For instance, stepping through the computation of a definite integral on one of these calculators might involve inputting the function, setting the lower and upper bounds of integration, and then letting the calculator evaluate the integral.
The correct option for the calculator function that computes definite integrals step by step is Option D) Definite integration.