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What is an integral

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What is an integral

1. 1. What is an integral?<br />
2. 2. Integrals<br />Another word for integral is the anti-derivative, basically an integral will take you derivative and make it back into your original function<br />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<br />
3. 3. Displacement and area<br />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<br />The height of the green rectangle is the displacement of the graph from x one to x two<br />X1 X2<br />
4. 4. Displacement and area<br />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<br />The height of the orange rectangle is the area of the derivative of the original (and pictured) function<br />X1 X2<br />
5. 5. Displacement and area<br />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<br />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. <br />X1 X2<br />