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

Average Value=1b−a∫abf(x),dx\text{Average Value} = \frac{1}{b-a} \int_{a}^{b} f(x) , dxAverage Value=b−a1​∫ab​f(x),dx

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

Average Value=1b−a∫abf(x),dx\text{Average Value} = \frac{1}{b-a} \int_{a}^{b} f(x) , dxAverage Value=b−a1​∫ab​f(x),dx

How do you calculate the area under a curve?

∫abf(x),dx\int_{a}^{b} f(x) , dx∫ab​f(x),dx

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

  1. Set up the integral: ∫abf(x),dx\int_{a}^{b} f(x) , dx∫ab​f(x),dx. 2. Multiply by 1b−a\frac{1}{b-a}b−a1​. 3. Evaluate the expression.

How to setup the average value integral?

Identify the interval [a,b] and the function f(x). Then setup: 1b−a∫abf(x),dx\frac{1}{b-a} \int_{a}^{b} f(x) , dxb−a1​∫ab​f(x),dx

Define the average value of a function.

The average y-value of a function over a given interval.

What does 'continuous on [a,b]' mean?

The function has no breaks, jumps, or undefined points on the closed interval from a to b.

Define definite integral.

The definite integral of a function f(x) from a to b represents the net signed area between the curve of f(x) and the x-axis from x=a to x=b.