# Definite Integral Introduction & Approximation

- Author:
- Dr. Jack L. Jackson II

- Topic:
- Definite Integral

## Area Problem

## Left Riemann Sum

## Right Riemann Sum

## Too Large or Too Small?

When do the Left and Right Riemann Sums perfectly find the actual exact area? When are they definitely too large, and when are they definitely too small?

## Better Estimate?

Why is the answer to the last question good news? How can we combine the Left and Right Riemann Sum estimates to get a better estimate?

## Trapezoidal Rule

Why is it called the Trapezoidal Rule?

## Midpoint Rule

Can we visualize the Midpoint Rule with trapezoids?

## Too Big or Too Little?

Show only the Midpoint Rule Trapezoids and the Trapezoid Rule Trapezoids. When are these estimates perfect? When are they too large, and when are they too small?

Which of the two gives a better estimate, the Trapezoidal Rule or the Midpoint Rule. Look carefully at the graphs with the Trapezoid Rule Trapezoids and Midpoint Rule Trapezoids turned on.

## Simpson's Rule

## Increasing n

What happens to our estimates as we increase the value of n?

What Calculus concept are we talking about here?