Suppose you estimate the area under the graph of f(x)=x^3 from x=9 to x=29 by adding the areas of rectangles as follows: partition the interval into 20 equal subintervals and use the right endpoint of each interval to determine the height of the rectangle. What is the area of the 13th rectangle?

So what I did is (29-9)/20 which would equal 1 so then I had my final problem as (29+2*12)=148877 which is not right. Ideas?

Question

Suppose you estimate the area under the graph of f(x)=x^3 from x=9 to x=29 by adding the areas of rectangles as follows: partition the interval into 20 equal subintervals and use the right endpoint of each interval to determine the height of the rectangle. What is the area of the 13th rectangle?

So what I did is (29-9)/20 which would equal 1 so then I had my final problem as (29+2*12)=148877 which is not right. Ideas?

ddcamp · Answer

If you have 20 rectangles, each will have a width of 1, sort of like this:
|dw:1384485792578:dw|
The problem is asking for the area of just the 13th triangle. What would be the height of this rectangle?