To find the area under a curve, we can use different methods that are important in AP Calculus AB. Here are some simple ways to do it:

1. Riemann Sums: This method breaks down the area under the curve into rectangles. You can choose to measure the height of the rectangles in three different ways:

   • Left Endpoint: Look at the height on the left side of each small section.
   • Right Endpoint: Look at the height on the right side.
   • Midpoint: Measure the height right in the middle of each small section.

2. Trapezoidal Rule: This method is a bit different. Instead of rectangles, it uses trapezoids to get a better estimate of the area: $\text{Area} \approx \frac{b-a}{n} \left( \frac{f(a) + f(b)}{2} + \sum_{i=1}^{n-1} f(x_i) \right)$

3. Integral Calculus: To find the exact area under a curve from point $x=a$ to $x=b$, we use something called the definite integral: $\text{Area} = \int_a^b f(x) \, dx$

These methods make it easier for us to see and calculate the area under a curve!