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Session 2: Integration

Completion requirements

The figure shows a set of Cartesian axes labelled x and y concentrated mainly in the upper-right quadrant. The graph of y equals f of x is shown which passes through the origin from the lower-left quadrant and has two local maximum points and one local minimum. The points x sub zero equals a is marked on the positive x-axis and is close to the origin. The point x sub one is marked on the positive x-axis and is further from the origin. The point x sub n equals b is marked on the positive x-axis and is further away still. There is an ellipses shown on the positive x-axis to demonstrate the sequence x sub zero to x sub n. There are five consecutive touching rectangles under the curve which have base along the horizontal axis. The base of the first rectangle goes from x sub 0 to x sub1 and its height is from x sub 1 to the curve of y equals f of x. The subsequent four rectangles each have arbitrary width and height which is determined by the right-hand side of the rectangle intersecting the curve. The final rectangle’s right-hand side is at x sub n.