1. What is an integral?

2. Integrals Another word for integral is the anti-derivative, basically an integral will take you derivative and make it back into your original function Integrals also find the area between a curve and the x-axis, and through this they can find the displacement or change in y from your original function of x value to another

3. Displacement and area Displacement means the change in y value, and an integral will always find the change in y value from one x to another of the original function The height of the green rectangle is the displacement of the graph from x one to x two X1 X2

4. Displacement and area Area is the “distance” the original function travels along the y axis, essentially it is the highest value the function ever reaches minus the lowest value the function ever reaches The height of the orange rectangle is the area of the derivative of the original (and pictured) function X1 X2

5. Displacement and area To find the area of a function you must split up the derivative where the derivative goes beneath the x axis. You then take the absolute value of the integrals from each portion of the graph The area between the derivative (shown) and the x axis, the area in blue, would tell the area or total distance the original function traveled. X1 X2