The Definite Integral, Area and Riemann Sums

How do we calculate the (signed) area under a curve, say y = f(x) which is bounded by x=a to the left, x = b to the right, and the x-axis? Click the check boxes and adjust the number of boxes n and location of the sample point to see various approximations of the area.

How to use this demo:
- Drag a and b along the x-axis to change the left- and right-hand sides of the definite integral.
- Change n by dragging the slider back and forth to change the number of boxes in the approximation.
- Change the sampled value of f within each box's interval by dragging the upper slider back and forth. You can see left-, midpoint, and right-hand sums this way.
- Type "f(x) = x^2 + 1" or any function of your choice into the Input Bar to run the demo for other functions.

Jason McCullough, Created with GeoGebra