Question

How do you evaluate the definite integral using the limit process?

a) Riemann Sums
b) Trapezoidal Rule
c) Simpson's Rule
d) Mean Value Theorem

Answer 1

To evaluate the definite integral using the limit process, you can use methods such as Riemann Sums, Trapezoidal Rule, Simpson's Rule, or the Mean Value Theorem.

Step-by-step explanation:

To evaluate the definite integral using the limit process, we can use various methods such as Riemann Sums, Trapezoidal Rule, Simpson's Rule, or the Mean Value Theorem. Here is a step-by-step explanation for each method:

1. Riemann Sums: Divide the interval into subintervals, calculate the function's values at each subinterval, multiply them by the width of the subinterval, and sum them up.
2. Trapezoidal Rule: Similar to Riemann Sums, divide the interval into subintervals, but instead of using rectangles, use trapezoids to approximate the area under the curve.
3. Simpson's Rule: Divide the interval into an even number of subintervals, calculate the function's values at each subinterval, and use a specific formula to calculate the integral.
4. Mean Value Theorem: Find a value within the interval where the instantaneous rate of change equals the average rate of change.