Approximating the area

Question

Estimate the area under the graph of y=x2+6x for x between 0 and 2. Use a partition that consists of 4 equal subintervals of [0, 2] and use the right endpoint of each subinterval as a sample point.

 

 

Answer 1

1) sub-intervals: [0,.5], [.5,1], [1,1.5], [1.5,2], each has a width of 0.5

2) height is the y-value of y=x² +6x at the right end of each sub-interval: 3.25, 7, 11.25, 16

3) multiply each height by the width, 0.5, and add them together, or add then multiply:

   .5(3.25+7+11.25+16) = 18.75