To find the average value of a function using a special math rule called the Mean Value Theorem for Integrals, just follow these simple steps:
Pick Your Function: Start by choosing the function (f(x)) that you want to work with. Make sure it's over a specific range, or interval, which we call ([a, b]).
Do the Integral Math: Next, calculate the area under the curve of your function by finding the definite integral:
[
\int_a^b f(x) , dx.
]
Use the Average Value Formula: Now, apply the formula for finding the average value:
[
\text{Average Value} = \frac{1}{b-a} \int_a^b f(x) , dx.
]
This formula helps you see what “average” means when you’re looking at the area under the curve of your function!
To find the average value of a function using a special math rule called the Mean Value Theorem for Integrals, just follow these simple steps:
Pick Your Function: Start by choosing the function (f(x)) that you want to work with. Make sure it's over a specific range, or interval, which we call ([a, b]).
Do the Integral Math: Next, calculate the area under the curve of your function by finding the definite integral:
[
\int_a^b f(x) , dx.
]
Use the Average Value Formula: Now, apply the formula for finding the average value:
[
\text{Average Value} = \frac{1}{b-a} \int_a^b f(x) , dx.
]
This formula helps you see what “average” means when you’re looking at the area under the curve of your function!