Consider the following.

Question

(a) By reading values from the given graph of f, use five rectangles to find a lower estimate for the area under the given graph of f from x = 0 to x = 10. (Round your answer to one decimal place.)

By reading values from the given graph of f, use five rectangles to find an upper estimate for the area under the given graph of f from x = 0 to x = 10. (Round your answer to one decimal place.)

(b) Find new estimates using ten rectangles in each case. (Round your answers to one decimal place.) (lower limit and upper limit)

Answer 1

These are left and right Riemann sums

For the first, lower estimate = 2 ( f(2) + f(4) + f(6) + f(8) + f(10)) { as the function is decreasing }

For the upper estimate 2 ( f(0) + f(2) + f(4) + f(6) + f(8))

Then for the 10 rectangles

Lower 1 ( f(1) + f(2) + ... f(10))

Upper 1 ( f(0) + f(1) + ... f(9))