All Flashcards

Steps to find the average value of f(x) on [a, b]?

Set up the integral: $\int_{a}^{b} f(x) , dx$ . 2. Multiply by $\frac{1}{b-a}$ . 3. Evaluate the expression.

How to setup the average value integral?

Identify the interval [a,b] and the function f(x). Then setup: $\frac{1}{b-a} \int_{a}^{b} f(x) , dx$

What is the formula for the average value of a function f(x) on the interval [a, b]?

$\text{Average Value} = \frac{1}{b-a} \int_{a}^{b} f(x) , dx$

How do you calculate the area under a curve?

$\int_{a}^{b} f(x) , dx$

Explain the concept of the average value of a function.

It finds the height of a rectangle with the same width (b-a) as the interval [a, b] that has the same area as the area under the curve of the function on that interval.

What does the integral $\int_{a}^{b} f(x) , dx$ represent?

The area under the curve of f(x) from x=a to x=b.

Why is continuity important when finding the average value?

Continuity ensures that the definite integral exists and that the average value can be accurately calculated.