Question

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. (4 points)
I got 34. I'm I right?

Answer 1

We need to find the lowest values
the length is (3-0)/3=3/3=1 width
area=length times width, since all are 1, just add the heights

evaluate f(0) and f(1) and f(2) and f(3)
find the one that is the lower one and use that one
f(0)=16
f(1)=15
f(2)=12
f(3)=7

for f(0) and f(1)
f(1) is lower so the height for this one is f(1) or 15 is height

for f(1) and f(2)
f(2) is lower so height is f(2) or 12

for f(2) and f(3)
f(3) is lower so height is f(3) or 7


15+12+7=34
yep you're right