Bluegrass Community & Technical College Area Under the Curve Graphic Calculations

I’m working on a calculus multi-part question and need support to help me understand better.

Graph f(x) = (x+1)(x-1)(x+2)(x-2)(x-3) and use the curve for the questions

You may want to print multiple copies and draw on the copies for this activity. Taking pictures of your drawings will suffice when you turn it in (as long as I can see them).

1. Draw rectangles of width 1 unit

Notice in the example above how I drew each rectangle with width one so that the right side of the rectangle hit the curve.
Once you have drawn your rectangles in this way, calculate the sum of all of the areas of the rectangles.

1. Do the same thing you did for number 1, but draw your rectangles by letting the left side of the rectangle touch the curve. Find the sum of the areas.
2. Do the same thing you did for number 1, but draw your rectangles with a width of 1?2 unit and the right side of the rectangle will determine the height of the rectangle.
3. Do the same thing you did for number 2, but draw your rectangles with a width of 1?2 unit and the left side of the rectangle will determine the height of the rectangle.
4. Use integration to find the actual area between the curve and the x-axis. Note: you will do four integration problems (each part above will be an integration and each part below the x-axis will be a problem).