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Question 1206999: Use upper rectangles with areas equal to f(x). Δx to estimate the area under the curve of f(x) = x², on the interval [2,4]. Partition the interval into 4 subintervals.
Hint: Don't spend time graphing the function unless you really want to. Your 4 rectangles should have heights equal to f(2.5), f(3), f(3.5) and f(4).
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
What is it about this that you need help with? The statement of the problem tells you practically everything you need to find the answer -- you just need to do the work.
The interval [2,4] has width 2; divided into four subintervals, the width of each subinterval -- and so the width of each rectangle -- is 0.5.
As given in the problem, the heights of the rectangles are f(2.5), f(3), f(3.5) and f(4).
The area of each rectangle, as shown in the statement of the problem, is the function value at the right end of each subinterval, times the width of each rectangle. The area estimate is the sum of the areas of the four rectangles.
You can do the calculations....
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