Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x

Question

Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval.

 

f(x) = 2x + 3, [0, 2], 4 rectangles

?  < Area <  ?

 

Answer 1

Answer:  9 < A < 11;  note that exact answer (area of trapezoid) is:  A = 10

 

details of the above answer, with f(x) = 2x + 3:

 

using inscribed rectangles:  A1 = 0.5[f(0) + f(0.5) + f(1) + f(1.5)] = 0.5[3 + 4 + 5 + 6 ] = 9

 

using circumscribed rectangles:  A2 = 0.5[f(0.5) + f(1) + f(1.5) + f(2)] = 0.5[4 + 5 + 6 + 7] = 11