Estimate the area under the curve f(x)=16-x^2 from x=0 to x=3 by using three inscribed (under the curve) rectangles. Answer to the nearest integer.

Answer 1

so the width of each of the 3 rectangles from x = 0 to 3 is 1 unit
the height, when x = 1 is 15
the height, when x = 2 is 12
the height, when x = 3 is 7

so the estimated area = 1x15 + 1x12 + 1x7 = 34 square units

real answer:
∫ 16-x^2 dx from 0 to 3
= [16x - x^3 /3] from 0 to 3
= 48 - 9 - 0 = 39

Answer 2

again with the Riemann sums?
Google for an online calculator, or read examples from online or your text.

Answer 3

just did this quiz and the answer is 34. 39 is wrong because that is the actual area, and the question says inscribed, which is an underestimate of the actual area. if it asked for circumscribed the answer would be an overestimate of the actual area (39) and would be 43.