Answer:
43
Step-by-step explanation:
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
First we find out the width of the rectangle
Δx=b−a/n, a= 0 and b= 3, n= 3
so Δx= 1
Divide the interval [0,3] into 3 sub intervals of width=1
[0,1] [1,2] [2,3]
Now we plug in end point and evaluate the function
We take left endpoints
f(0) = 16 - 0^2=16
f(1) = 16 - 1^2= 15
f(2) = 16 - 2^2= 12
Now sum = Δx(f(0) + f(1)+f(2))
= 1 (16+15+12)= 43