Approximating the area

Question

Estimate the area under the graph of y=7x for x between 0 and 2. Use a partition that consists of 4 equal subintervals of [0, 2] and use the left endpoint of each subinterval as a sample point.

The answer is not 5.25, 16, or 14

Answer 1

1) If your sub-intervals are [0,.5], [.5,1], [1,1.5], [1.5,2], each has a width of .5.

2) Since the directions say to use the left end of the sub-interval as the sample point,

    we use the y values from y=7x at 0, .5, 1, and 1.5 for the height of each sub-interval, respectively.

    The height of the first sub-interval is thus 0, the second 3.5, the third 7, and the fourth 10.5.

3) You then multiply each height by the width, 0.5, and add them together.

 

.5(0)+.5(3.5)+.5(7)+.5(10.5)=10.5