Area Under a Curve (Linear). Find the area bounded by the x-axis, y = x and x =1. 1. Divide the x-axis from 0 to 1 into n equal parts. 2. Subdividing.

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Presentation transcript:

Area Under a Curve (Linear)

Find the area bounded by the x-axis, y = x and x =1. 1. Divide the x-axis from 0 to 1 into n equal parts. 2. Subdividing will occur at

3. Within any sub-interval, the function y = x has a minimum value at the beginning of the interval and a maximum value at the end of the interval. 4. Write an expression for the sum of the areas of the rectangles where the width of each rectangle is the width of the sub- interval and the height is the minimum value of the function in that sub-interval.

Sub-intervalHW Area (B n -1 )

If rectangles are drawn so that they touch the curve at their upper right corner then the rectangles are above the curve and we have B n +