Calculus
posted by Daniel on .
Estimate the area under the graph of 25−x 2 from x = 0 to x = 5 using 5 left rectangles.
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.

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