Estimate the area under the graph of 25−x 2 from x = 0 to x = 5 using 5 left rectangles.

Question

b. Sketch for yourself the graph of f and the rectangles. Is this left sum an overestimate or underestimate? Enter OVER or UNDER.

c. Now use 5 right rectangles to estimate the area.

d. Is the right sum you got an overestimate or underestimate? Enter OVER or UNDER.

Answer 1

y = 25 - x^2

x _____ y

0 _____ 25

1 _____ 24

2 _____ 21

3 _____ 16

4 _____ 11

delta x = 1
so
25 + 24 + 21 +16 + 11 = 97

b the rectangles are all ABOVE the curve, so the estimate is OVER

c do it now with x = 1, 2, 3, 4, 5
these rectangles are below the curve so under estimate

real answer by the way:
integral from x = 0 to x = 5 of 25-x^2

25 x - (1/3)x^3 at 5 - at 0
125 - (1/3)(125) = (2/3)(125) =83 1/3