What is an integral

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 X 1 X 2 The height of the green rectangle is the displacement of the graph from x one to x two

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 X 1 X 2 The height of the orange rectangle is the area of the derivative of the original (and pictured) function

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 X 1 X 2 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.